6. sue goes to the bakery and purchases cupcakes and cookies for a picnic. she needs to serve 36 people. cupcakes cost $2.50 each, cookies cost $1.00 each. she spends $54.00. how many cupcakes did she purchase?

She purchased 24 cupcakes

If she needs to serve 36 people, then;

x + y = 36  1

if cupcakes cost $2.50 each, cookies cost $1.00 each while she spends $54.00, then;

2.5x + y = 54 2

From equation 1, x = 36 - y

Substitute into equation 2;

2.5(36-y) + y = 54

90 - 2.5y + y = 54

-1.5y = - 36

y = 36/1.5

y = 24

Hence she purchased 24 cupcakes

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the number of cupcakes that Sue purchased is 12

Step-by-step explanation:

Let x represent the number of cupcakes that Sue purchased at the bakery.

Let y represent the number of cookies that Sue purchased at the bakery.

She needs to serve 36 people. This means she would purchase a total of 36 people. Therefore,

x + y = 36

Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. This means that

2.5x + y = 54 - - - - - - - - - 1

Substituting x = 36 - y into equation 1, it becomes

2.5(36 - y) + y = 54

90 - 2.5y + y = 54

- 2.5y + y = 54 - 90

- 1.5y = - 36

y = - 36/ - 1.5

y = =24

x = 36 - y = 36 - 24 = 12