This document contains solutions to two math word problems. The first problem involves determining the price of shoes and sandals given information about how many pairs of each were purchased and the total amount spent. The second problem involves determining the current ages of a father and son given their age difference now and the sum of their ages five years ago. Both problems are set up as systems of linear equations that are then solved using substitution to find the individual ages or prices requested.

1. 11th
Meeting
Example 1:
Given a pair of shoes price is twice of a pair of sandals price. A seller buys 4 pairs of shoes
and 3 pairs of sandals. He has to pay Rp 275.000,00. Determine the price of 3 pairs of
shoes and 2 pairs of sandals!
Solution:
Let a pair of shoes price is equal to x and a pair of sandals price is equal to y.
From the given, we obtain that:
*) a pair of shoes price is twice of a pair of sandals price,
Then the equation is
*) a seller buys 4 pairs of shoes and 3 pairs of sandals with Rp 275.000,
Then the equation is
By substituting method, we obtain,
Then,
Hence, a pair of shoes price is Rp ................. and a pair of sandals price is Rp ....................
We are interested to find the price of 3 pairs of shoes and 2 pairs of sandals, then we obtain
mathematics model as
Such that,
Therefore,
The price of 3 pairs of shoes and 2 pairs of sandals is Rp ..........................

2. Example 2
Given the difference age between a father and his son now is 26 years, meanwhile five
years ago the both sum of their age is 34 years. Determine each of father’s age and his
son’s age two years later!
Solution:
Let father’s age now be equal to x and son’s age now be equal to y.
From the given, we obtain that:
*) difference age between a father and his son now is 26 years
Then the equation is
*) five years ago the both (father’s age and his son’s age) sum of their age is 34 years
Then the equation is
We obtain two linear equations system with two variables are:
(1)
(2)
Then we solve them by substitution-elimination method as follows,
By using elimination method, we eliminate y,
We have x = 35, and we substitute into the (1) equation, then
Hence,
x = 35 and y = 9
Since we asked to determine father’s age and his son’s age two years later, then we have
x + 2 = 35 + 2 = 37
y + 2 = 9 + 2 = 11
Therefore,
For two years later, father’s age is 37 years and his son’s age is 11 years