Granola costs $4.50 per pound. Assorted nuts cost $7 per pound. How many pounds of granola and nuts are needed to make 7 pounds of trail mix that costs $6 per pound?

Answer 1

Let x be the number of pounds of granola needed and y be the number of pounds of assorted nuts needed to make 7 pounds of trail mix.

Since the total weight of trail mix is 7 pounds, we have:

x + y = 7 (equation 1)

Let's express the cost of trail mix in terms of the cost per pound of granola and assorted nuts.

The cost per pound of the trail mix is $6, which means that the total cost of 7 pounds of trail mix is:

7($6) = $42

Since granola costs $4.50 per pound and assorted nuts cost $7 per pound, the cost of the trail mix can also be expressed as:

4.5x + 7y = $42 (equation 2)

We now have two equations with two variables. We can solve for x and y using substitution or elimination.

Using substitution, we can solve equation 1 for x in terms of y:

x = 7 - y

Substituting this expression for x into equation 2, we get:

4.5(7 - y) + 7y = $42

Simplifying and solving for y, we get:

31.5 - 2.5y + 7y = $42

4.5y = $10.5

y = 2.33

Substituting this value of y back into the equation x + y = 7, we get:

x + 2.33 = 7

x = 4.67

Therefore, we need 4.67 pounds of granola and 2.33 pounds of assorted nuts to make 7 pounds of trail mix that costs $6 per pound. Since we cannot have fractional amounts of ingredients, we can round up the number of pounds of assorted nuts to 3 and adjust the amount of granola accordingly, giving:

x = 7 - y = 7 - 3 = 4

So, we need 4 pounds of granola and 3 pounds of assorted nuts to make 7 pounds of trail mix that costs $6 per pound.

Answer 2