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:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq