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7nadin3 [17]
3 years ago
12

Nuts Galore sells a trail mix containing dried banana chips, roasted almonds, and chocolate chips that sells for $6.52 per pound

. The dried banana chips costs $4 per pound, the roasted almonds cost $8 per pound, and the chocolate chips cost $6 per pound. The amount of roasted almonds used is three times the amount of chocolate chips used. If they plan to make 100 pounds of this trail mix, how many pounds of each ingredient should be used
Mathematics
1 answer:
KengaRu [80]3 years ago
6 0

Answer:

x = 28 ----- Banana

y = 54 ----- Almonds

z = 18 ---- Chocolate

Step-by-step explanation:

Let

x \to banana

y \to almonds

z \to chocolate

So, we have:

x + y + z = 100 --- total used

4x + 8y + 6z = 652 -- i.e. 6.52 * 100 --- total sales from 100 pounds

y = 3z

Required

The number of pounds of each (i.e. x, y and z)

Substitute y = 3z in x + y + z = 100

x + 3z + z = 100

x + 4z = 100

Make x the subject

x = 100 - 4z

Substitute y = 3z in 4x + 8y + 6z = 652

4x + 8 * 3z + 6z = 652

4x + 24z + 6z = 652

4x + 30z = 652

Substitute x = 100 - 4z

4(100 - 4z) + 30z = 652

400 - 16z + 30z = 652

Collect like terms

- 16z + 30z = 652-400

14z = 252

Divide by 14

z = 18

Substitute z = 18 in x = 100 - 4z

x = 100 - 4 * 18

x = 100 - 72

x = 28

To calculate y, we have:

y = 3z

y = 3 * 18

y = 54

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