Question

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?

Answer 1

Answer:

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.

!!

Answer 2

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

• Let the candies be C.

• Let the nuts be N.

Given the following data:

• Cost of candies per cup = $2.49

• Cost of nuts per cup = $0.69

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

For total number of cups:

$C + N = 12$  .....equation 1

For cost of candies and nuts:

$2.49C + 0.69N = 1.29(12)\\\\2.49C + 0.69N = 15.48$.....equation 2

From equation1:

$C = 12 - N$   ....equation 3

Substituting eqn 3 into eqn 1, we have:

$2.49(12 - N) + 0.69N = 15.48\\\\29.88 - 2.49N + 0.69N = 15.48\\\\1.8N = 29.88 - 15.48\\\\1.8N = 14.4\\\\N = \frac{14.4}{1.8}$

Number of nuts, N = 8 cups

For candies:

$C = 12 - N\\\\C = 12 - 8$

Number of candies, N = 4 cups

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