Question

Carter and his children went into a bakery where they sell cupcakes for $3 each and

cookies for $0.50 each. Carter has $35 to spend and must buy a minimum of 15
cupcakes and cookies altogether. If x represents the number of cupcakes purchased
and y represents the number of cookies purchased, write and solve a system of
inequalities graphically and determine one possible solution. (I need 2 inequality’s)

Answer 1

Answer:
3x + 0.5y = 35
x + y >/= 15

Possible solution: (11, 4)
11 cupcakes, 4 cookies
____________
Cupcakes = x
Cookies = y

Cupcakes are $3 each —> 3x
Cookies are $0.50 each —> 0.5y

$35 to spend: less than or equal to =
3x + 0.5y = 35

Minimum of 15: greater than or equal to >/= 15

x + y >/= 15
____________

3x + 0.5y = 35
x + y >/= 15

Solve second for y:
y >/= 15 - x

Substitute into first:
3x + 0.5(15 - x) = 35
3x + 7.5 - 0.5x = 35

Combine like terms
2.5x + 7.5 = 35

Subtract 7.5
2.5x = 27.5

Divide by 2.5
x is less than or equal to 11

So y is less than or equal to 4

Check:
4 + 11 = 15 :)

3*11 + 0.5*4 = 35
33 + 2 = 35
35 = 35 :)