word problem help

Question

A trail mix that costs $2.45 per pound is mixed with a trail mix that costs $2.30 per pound. How much of each type of trail mix must be used to have 30 pounds of a trail mix that costs $2.35 per pound?

Answer 1

Hi,

This is a systems of equations problem where you are given enough information to set up two equations for two variables.

Let x=the amount (lbs) of the first trail mix that costs $2.45/lb.

Let y=the amount (lbs) of the second trail mix that costs $2.30/lb.

 

You want to find x and y given that:

x + y = 30 lbs (total amount of mixed trail mix)

 

and that

$2.45x + $2.30y = $2.35 (30)  the cost of each trail mix type added together to equal the final cost

 

2.45x + 2.3y = 70.5

 

You now have two equations in terms of x and y that can be solved using substitution or elimination. Let's try substitution. 

x + y = 30

2.45x + 2.3y = 70.5

 

You can easily subtract x from both sides of the first equation, and get y = 30 - x. Substitute this equation into the second equation in place of y

 

2.45x + 2.3 (30 - x) = 70.5 or (using the distributive property) 2.45x + 2.3(30) - 2.3x = 70.5

 

Group like terms by rearranging and subtracting 2.3(30) = 69 from both sides of the equation

2.45x - 2.3x + 69 = 70.5

                     -69   -69

 

2.45x - 2.3x = 1.5

 

0.15x = 1.5, now divide each side of the equation by 0.15 and get x alone and then solve for x

 

0.15 x/ 0.15 = 1.5/0.15

 

x = 10 

 

use x + y = 30 and substitute in 10 for x, then  10 + y = 30, subtract 10 from each side and solve for y. y = 20.

 

So the answer to the problem is 

x=the amount (lbs) of the first trail mix that costs $2.45/lb. = 10 lbs
y=the amount (lbs) of the second trail mix that costs $2.30/lb. = 20 lbs.