Question

For a camping trip, Blake wants to make a trail mix of almonds, walnuts and raisins. He wants one part almonds, two parts walnuts, and three parts raisins. Almonds cost $15 per pound, walnuts cost $10 per pound, and raisins cost $5 per pound. Blake has $30 to spend on the trail mix. The equation 15x + 10(2x) + 5(3x) = 30 models the pounds, x. How many pounds of trail mix can Blake buy?

Answer 1

We are given equation: 15x + 10(2x) + 5(3x) = 30.

Where x represents number of pounds.

Almost cost =  $15 per pound.

Therefore, cost of x pounds of almonds = 15*x = 15x .

Walnuts cost = $10 per pound.

We have two parts walnuts.

Therefore, cost of 2 times x pounds of walnuts = 10*(2x).

Raisins cost = $5 per pound.

We are given three parts raisins.

Therefore, cost of 3 times x pounds of raisnis = 5*(3x).

Total money spent = $30.

Let us solve the given equation for x now.

15x + 10(2x) + 5(3x) = 30.

15x + 20x +15x = 30.

Combining like terms, we get

50x = 30.

Dividing both sides by 50, we get

50x/50 = 30/50.

x=0.6

Therefore, number of pounds of Almonds = 0.6 pound.

Walnuts = 2x = 2*0.6 = 1.20 pounds.

Raisins = 3x = 3*0.6 = 1.80 pounds.

Therefore, total number of pounds of  trail mix can Blake buy = 0.6 + 1.20 + 1.80 = 3.60 pounds.