Here are the key steps to solve this problem: * Let x = ounces of 2% acid solution * Then 20 - x = ounces of 4% acid solution * Set up an equation relating the percentage of acid in each part to the total percentage in the final solution: (0.02x + 0.04(20-x))/20 = 0.036 * Solve the equation for x * The answer is the number of ounces of 2% acid solution to use So in summary: - Let x = ounces of 2% solution - 20 - x = ounces of 4% solution - Set up and solve equation relating percentages to get x - The value of x

1. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?

2. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.

3. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.

4. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.

5. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.
So x - y represents the speed of the boat against the current.

6. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.
So x - y represents the speed of the boat against the current.
Remember that distance = speed x time & make your system:

7. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.
So x - y represents the speed of the boat against the current.
Remember that distance = speed x time & make your system:
20 = (x + y)2.5

20 = (x − y)3

8. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.
So x - y represents the speed of the boat against the current.
Remember that distance = speed x time & make your system:
20 = (x + y)2.5

20 = (x − y)3
(22/3, 2/3)

9. p. 358/6 Chris can row a boat a distance of 20 miles in 2.5 hours when he is
rowing with the current. It takes him 3 hours to row the same distance when
he is rowing against the current. What is the rate of the current?
Let x represent the speed of the boat with no current.
Let y represent the speed of the current.
So x + y represents the speed of the boat with the current.
So x - y represents the speed of the boat against the current.
Remember that distance = speed x time & make your system:
20 = (x + y)2.5

20 = (x − y)3
(22/3, 2/3)
So, the current is
2/3 miles/hour.

10. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?

11. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.

12. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.

13. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.
Since each nickel is worth 5 cents, the x nickels are worth
0.05x dollars, and since each quarter is worth 25 cents, the
y quarters are worth 0.25y dollars.

14. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.
Since each nickel is worth 5 cents, the x nickels are worth
0.05x dollars, and since each quarter is worth 25 cents, the
y quarters are worth 0.25y dollars.
Use the total number 20 to make one equation and the total
value $2.60 to make another.

15. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.
Since each nickel is worth 5 cents, the x nickels are worth
0.05x dollars, and since each quarter is worth 25 cents, the
y quarters are worth 0.25y dollars.
Use the total number 20 to make one equation and the total
value $2.60 to make another.
20 = x + y

2.60 = 0.05x + 0.25y

16. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.
Since each nickel is worth 5 cents, the x nickels are worth
0.05x dollars, and since each quarter is worth 25 cents, the
y quarters are worth 0.25y dollars.
Use the total number 20 to make one equation and the total
value $2.60 to make another.
20 = x + y
 (12, 8)
2.60 = 0.05x + 0.25y

17. p. 358/8 When Jim cleaned out the reflecting pool at the library, he found 20
nickels and quarters. The collection of nickels and quarters totaled $2.60. How
many quarters did Jim find?
Let x represent the number of nickels Jim found.
Let y represent the number of quarters Jim found.
Since each nickel is worth 5 cents, the x nickels are worth
0.05x dollars, and since each quarter is worth 25 cents, the
y quarters are worth 0.25y dollars.
Use the total number 20 to make one equation and the total
value $2.60 to make another.
20 = x + y
 (12, 8)
2.60 = 0.05x + 0.25y
So, Jim found 8
quarters.

18. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?

19. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.

20. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.

21. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.

22. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.
The first sentence gives the first equation.

23. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.
The first sentence gives the first equation.
The second sentence gives the second equation (be careful,
though- 1 less than the second digit is y - 1, not 1 - y!)

24. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.
The first sentence gives the first equation.
The second sentence gives the second equation (be careful,
though- 1 less than the second digit is y - 1, not 1 - y!)
 x + y = 13

2x = y − 1

25. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.
The first sentence gives the first equation.
The second sentence gives the second equation (be careful,
though- 1 less than the second digit is y - 1, not 1 - y!)
 x + y = 13

2x = y − 1 (4, 9)

26. p. 358/17 The sum of the digits of a positive two-digit number is 13. If twice
the first digit is 1 less than the second digit, what is the two digit number?
Let x represent the tens digit of the number.
Let y represent the units digit of the number.
So, 10x + y represents the two digit number.
The first sentence gives the first equation.
The second sentence gives the second equation (be careful,
though- 1 less than the second digit is y - 1, not 1 - y!)
 x + y = 13

2x = y − 1 (4, 9)
So, the number is
49.

27. Chemical Solution Problems
p. 357/Try This
How many ounces of a 2% acid
solution should be mixed with a 4%
acid solution to produce 20 ounces of
a 3.6% acid solution?