Question

Maria is mixing raisins and nuts to make 5 pounds of trail mix. Raisins cost $1.50, a pound and nuts cost $7 a pound. If Maria wants her cost for the trail mix to be $4.80 a pound, how many pounds of raisins and how many pounds of nuts should she use?

Answer 1

3 pounds of nuts, 2 pounds of raisins

Explanation:

Write the equation by adding the total values, and solve for x to find the number of pounds of nuts.

7x + 1.5(5-x) = 5(4.80)

7x + 7.5 - 1.5x = 24

5.5x = 16.5

x = 3

Answer 2

Maria should use 3 pounds of nuts and 2 pounds of raisins.

Explanation:

Givens

• Raisins cost $1.50 per pound.
• Nuts cost $7 per pound.
• Maria wants to make 5 pounds of trail mix, raisins and nuts all together.
• The cost of the trail mix will be $4.80 per pound.

Let's call raisins
`R` and nuts
`N`. Also,
`M` will express the mix.

We know that
`M = R + N`, because the mix is made from raisins and nuts. Where
`M=5`. So, the equation that represents this is

`R+N=5`

Now, the equation that represents the cost is

`1.50R+7N=4.80M` BUt,
`M=5`, so

`1.50R+7N=4.80(5)\\1.50R+7N=24`

Then, we isolate
`R` in the first equation to replace it into the second equation and solve for
`N`

`R+N=5\\R=5-N`

`1.50R+7N=24\\1.50(5-N)+7N=24\\7.5-1.50N+7N=24\\5.5N=24-7.5\\N=(16.5)/(5.5)\\ N=3`

Then, we replace this value in the first equation to find
`R`

`R+N=5\\R+3=5\\R=5-3\\R=2`

Therefore, Maria should use 3 pounds of nuts and 2 pounds of raisins.