Harry Styles wants to make trail mix made up of almonds, walnuts, and raisins. He wants to mix one part almonds, two parts walnuts and, three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound and, raisins cost $5 per pound.
He has $15 to spend on the trail mix. How many pounds of trail mix can he make?
a:w:r = 1:2:3
12(x) + 9(2x) + 5(3x) = 15
45x = 15
x = 1/3
so, he has
1/3 lb almonds
2/3 lb walnuts
1 lb raisins
check costs:
almonds (1/3)(12) = 4
walnuts (2/3)(9) = 6
raisins (1)(5) = 5
total: 15
To find out how many pounds of trail mix Harry can make, we need to determine how much each of the three ingredients will cost and then figure out the maximum quantity he can afford with his budget.
First, let's calculate the cost of each ingredient based on the given prices per pound:
- Almonds cost $12 per pound
- Walnuts cost $9 per pound
- Raisins cost $5 per pound
Since Harry's budget is $15, we can use this information to calculate the maximum quantity of each ingredient he can afford. Let's denote the quantities as:
- Almonds: x pounds
- Walnuts: 2x pounds (as he wants twice the amount of walnuts compared to almonds)
- Raisins: 3x pounds (as he wants three times the amount of raisins compared to almonds)
Now, let's calculate the total cost of the trail mix he wants to make:
Total cost = (cost of almonds) + (cost of walnuts) + (cost of raisins)
Total cost = (12 * x) + (9 * 2x) + (5 * 3x)
Total cost = 12x + 18x + 15x
Total cost = 45x
Since Harry's budget is $15, we can set up the following equation:
45x = 15
To solve for x, divide both sides of the equation by 45:
x = 15 / 45
x = 1/3
So, Harry can afford 1/3 of a pound of trail mix.
To find out how many pounds of trail mix this is, we can multiply the quantity of each ingredient by the value of x:
- Almonds: 1/3 pound
- Walnuts: 2/3 pound (2 * 1/3)
- Raisins: 1 pound (3 * 1/3)
Therefore, Harry can make 1/3 pound of trail mix, consisting of 1/3 pound of almonds, 2/3 pound of walnuts, and 1 pound of raisins.