Yumi wants to make 12 cups of party mix using candies and nuts. her budget requires the party mix to cost her $1.29 per cup. the candies are $2.49 per cup, and the nuts are $0.69 per cup. how many cups of candies and how many cups of nuts should she use?

The number of cups of candies and nuts, Yumi should use is 4 and 8 cups respectively.

Given the following data:

Translating the word problem into an algebraic expression, we have;

For total number of cups:

 .....equation 1

For cost of candies and nuts:

.....equation 2

From equation1:

  ....equation 3

Substituting eqn 3 into eqn 1, we have:

Number of nuts, N = 8 cups

For candies:

Number of candies, N = 4 cups

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4 cups of candies and 8 cups of nuts

Step-by-step explanation:

Cost per cup = $1.29

Total number of cups = 12

Total cost of cups = 12 x $1.29

                              = $15.48

Cost of candies = $2.49 per cup

Total number of candies = x

Cost of nuts = $0.69 per cup

Total number of nuts = y

Equations :

x + y = 12 (because total cups of nuts and candies will be equal to 12)

2.49x + 0.69y = 15.48 (Total cost of the 12 cups should be 15.48)

Step 1 : Find x in terms of y

x = 12 - y

Step 2 : substitute x in terms of y from step 1 in the second equation

2.49x + 0.69y = 15.48

2.49 ( 12 - y) + 0.69y = 15.48

29.88 - 2.49y + 0.69y = 15.48

-1.8y = -14.4

y = 14.4/1.8

y = 8

Step 3 : Find x

x + y = 12

x = 12 - y

x = 12- 8

x = 4

Yumi should use 4 cups of candies and 8 cups of nuts.

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step-by-step explanation:

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