Yumi wants to make 12 cups of party mix using candies and nuts her budget require the party mix to cost her $1 29 per cup. The candies are $ 2.49 per cup and nuts are 0.69 per cup how many cups of candiez and how many cups of nuts

Acording to the question,

Cost per cup = $1.29

Total number of cups = 12

Total cost of cups = 12 x 1.2 = $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

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

The highest common factor is 6

Step-by-step explanation:

Each of the two numbers needs to be expressed as a product of its prime factors. In this case:

12      = 2 × 2×3

1050 = 2 ×3×5×5×7

Taking the common numbers we find that the term (2 × 3) is common in both  expressions. Hence 2 × 3 = 6 is the highest common factor.