Question

coach thomas brings his baseball team to get ice cream after each friday night game. last week, he purchased 9 cones and 8 cups of ice cream and payed $53.50. this week he purchased 6 cones and 11 cups of ice cream and paid $51.25. write and solve a system of linear equations to determine the cost of each cone and each cup.

Explanation:

Step1: Define variables

Let $x$ = cost of 1 cone, $y$ = cost of 1 cup.

Step2: Set up linear equations

Last week: $9x + 8y = 53.50$
This week: $6x + 11y = 51.25$

Step3: Eliminate $x$ (scale equations)

Multiply first eq by 2: $18x + 16y = 107$
Multiply second eq by 3: $18x + 33y = 153.75$

Step4: Subtract equations

$(18x + 33y) - (18x + 16y) = 153.75 - 107$
$17y = 46.75$

Step5: Solve for $y$

$y = \frac{46.75}{17} = 2.75$

Step6: Substitute $y$ to find $x$

$9x + 8(2.75) = 53.50$
$9x + 22 = 53.50$
$9x = 53.50 - 22 = 31.50$
$x = \frac{31.50}{9} = 3.50$

Answer:

The cost of each cone is $\$3.50$ and the cost of each cup is $\$2.75$.