Question

Randall wants to mix 60lb of nuts worth 1$ per lb with some nuts worth 7$ per lb to make a mixture worth 6$ per lb. How many pounds of 7$ nuts must he use?

Answer 1

Given:

Table

To determine the amount of pounds of $7 nuts Randall must use, we use the equation below:

1(60)+7x=6(x+60)

where:

x = number of pounds of $7 nut required

We simplify the equation to get the value of x:

$\begin{gathered} 1\mleft(60\mright)+7x=6\mleft(x+60\mright) \\ \text{Simplify and rearrange} \\ 60+7x=6x+360 \\ 7x-6x=360-60 \\ x=300 \end{gathered}$

Hence, Randall needs 300 pounds of $7 nuts.

To complete the table, we apply the value of x:

Pounds of Nuts Cost per pound Total Cost

60 $1 60($1)=$60

x $7 300($7)=$2,100

60+x=60+300=360 $6 $60+$2,100=$2,160 or

360($6)=$2,160