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Monique and Tara each make an ice-cream sundae. Monique gets 4 scoops of Cherry ice-cream and 1 scoop of Mint Chocolate Chunk ice-cream for a total of 60g of fat. Tara has 1 scoop of Cherry and 4 scoops of Mint Chocolate Chunk for a total of 75g of fat. How many grams of fat does 1 scoop of each type of ice cream have?

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Answer:  

16 grams per scoop of Mint Chocolate

11 grams per scoop of Cherry

Step-by-step explanation:

4 scoops of cherry plus 1 scoop of mint chocolate = 60  

4 scoops of mint chocolate plus 1 scoop of cherry = 75

Set up a system of equations:

4c + m = 60

4m + c = 75 .  

reorganize the second equation to get a value for "c"  substitute in the fitst equation:  c= 75-4m

4c + m = 60

4(75 -4m) +m = 60 .Distribute  and solve

300 -16m + m = 60

300 - 60 = 16m + m

240 = 15m

240/15 = m

16 = m .  substitute in 4c + m = 60

4c + 16 = 60

4c= 60 - 16

4c = 44

c = 11

The factors in the word problem for the amount of fat in the ice cream

combination are given by the fat in each constituent.

  • The amount of fat in Cherry ice-cream is 11 grams.
  • The amount of fat in the Mint Chocolate Chunk ice-cream is 16 grams.

Reasons:

The given parameters are;

Let C represent the amount of fat in Cherry ice-cream, and let M represent

the amount of fat in Mint Chocolate Chunk ice-cream, we get;

4·C + M = 60...(1)

C + 4·M = 75...(2)

Multiplying equation (1) by 4 and then subtracting equation (2) from the

result gives;

4 × (4·C + M) = 4 × 60

16·C + 4·M = 240...(3)

(16·C + 4·M) - (C + 4·M) = 240 - 75

15·C = 165

[tex]C = \dfrac{165}{15} = 11[/tex]

The amount of fat in Cherry ice-cream C = 11 grams

4 × 11 + M = 60

M = 60 - 4 × 11 = 16

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 16 grams

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