Question

Man can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. She can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. How much does one box of crackers cost?

Answer 1

one box of crackers costs $0.70

Explanation:

Let $x be the price of 1 container of yogurt and $y be the price of 1 box of crackers.

1. Man can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. 4 containers of yogurt cost $4x and 3 boxes of crackers cost $3y. In total,

`3x+4y=9.55.`

2. Man can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. 2 containers of yogurt cost $2x and 2 boxes of crackers cost $2y. In total,

`2x+2y=5.90.`

3. Solve the system of two equations:

`\left\{\begin{array}{l}3x+4y=9.55\\2x+2y=5.90\end{array}\right.`

Multiply the second equation by 2 and subtract it from the first equation:

`3x+4y-2(2x+2y)=9.55-5.90\cdot 2,\\ \\3x+4y-4x-4y=9.55-11.80,\\ \\-x=-2.25,\\ \\x=\$2.25.`

Then

`2\cdot 2.25+2y=5.90,\\ \\2y=5.90-4.50,\\ \\2y=1.40,\\ \\y=\$0.70`