Find the amount of $0.76-per-lb candy to mix with $1.38-per-lb candy to create 8 lb of a $0.95-per-lb mixture.
STEP 1
Assumptions1. The first type of candy sells for \$0.76 per lb. The second type of candy sells for \$1.38 per lb3. We want to obtain8 lb of a mixture that sells for \$0.95 per lb4. The total weight of the two types of candy must add up to8 lb
STEP 2
Let's denote the weight of the \0.76perlbcandyasxandtheweightofthe$1.38perlbcandyasy.Weknowthatthetotalweightofthecandyis8lb,sowecanwritethefollowingequationx+y=8$
STEP 3
We also know that the total cost of the candy mixture should be \0.95perlb.Thismeansthatthetotalcostofthecandymixtureis$0.95∗8=$7.6.Wecanwriteanotherequationthatrepresentsthetotalcostofthecandymixture0.76x+1.38y=7.6$
STEP 4
Now we have a system of two equations with two variables that we can solve\begin{align*}
x + y &=8 \\
0.76x +1.38y &=7.6\end{align*}
STEP 5
To make the equations easier to solve, we can multiply the first equation by0.760.76x+0.76y=.08
STEP 6
Now we subtract the new equation from the second equation\begin{align*}
1.38y -0.76y &=.6 -6.08 \\
0.62y &=1.52\end{align*}
STEP 7
olving for y gives us the weight of the \1.38perlbcandyy=1.52/0.62≈2.45$
STEP 8
Substitute y=2.45 into the first equation to find the weight of the \0.76perlbcandyx+2.45=8$
STEP 9
olving for x gives us the weight of the \.76perlbcandyx=8−2.45=5.55$So, approximately5.55 lbs of candy that sells for \$.76 per lb must be mixed with approximately2.45 lbs of candy that sells for \$.38 per lb to obtain8 lbs of a mixture that should sell for \$.95 per lb.
