Answer: Let's call the number of sandals manufactured in a typical month x, and the number of running shoes manufactured in a typical month y. The total cost for sandals and running shoes in a typical month is $2450, so the following equation represents the cost:
2.5x + 4y = 2450
During the month of April, the company doubled the number of sandals manufactured, so x becomes 2x. The total cost during the month of April is $3700, so the following equation represents the cost:
2.5(2x) + 4y = 3700
Expanding the left side:
5x + 4y = 3700
Subtracting the first equation from the second equation:
5x - 2.5x + 4y - 4y = 3700 - 2450
2.5x = 1250
Dividing both sides by 2.5:
x = 500
Substituting x = 500 into the first equation:
2.5 * 500 + 4y = 2450
Expanding and solving for y:
1250 + 4y = 2450
1250 - 1250 + 4y = 2450 - 1250
4y = 1200
Dividing both sides by 4:
y = 300
So the company makes 500 pairs of sandals and 300 pairs of running shoes during a typical month.
Explanation: