Respuesta :
Answer:
3 pounds of nuts, 2 pounds of raisins
Step-by-step 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:
Maria should use 3 pounds of nuts and 2 pounds of raisins.
Step-by-step 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 [tex]R[/tex] and nuts [tex]N[/tex]. Also, [tex]M[/tex] will express the mix.
We know that [tex]M = R + N[/tex], because the mix is made from raisins and nuts. Where [tex]M=5[/tex]. So, the equation that represents this is
[tex]R+N=5[/tex]
Now, the equation that represents the cost is
[tex]1.50R+7N=4.80M[/tex] BUt, [tex]M=5[/tex], so
[tex]1.50R+7N=4.80(5)\\1.50R+7N=24[/tex]
Then, we isolate [tex]R[/tex] in the first equation to replace it into the second equation and solve for [tex]N[/tex]
[tex]R+N=5\\R=5-N[/tex]
[tex]1.50R+7N=24\\1.50(5-N)+7N=24\\7.5-1.50N+7N=24\\5.5N=24-7.5\\N=\frac{16.5}{5.5}\\ N=3[/tex]
Then, we replace this value in the first equation to find [tex]R[/tex]
[tex]R+N=5\\R+3=5\\R=5-3\\R=2[/tex]
Therefore, Maria should use 3 pounds of nuts and 2 pounds of raisins.
