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?

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

combination are given by the fat in each constituent.

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

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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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