Chapter 5: Q 180. (page 627)

Josie wants to make $10$ pounds of trail mix using nuts and raisins, and she wants the total cost of the trail mix to be $$54$ . Nuts cost $$ 6$ per pound and raisins cost $$ 3$ per pound. Solve the system $\{\begin{cases} n + r = 10 \\ 6 n + 3 r = 54 \end{cases}$ to find $n$ , the number of pounds of nuts, and $r$ , the number of pounds of raisins she should use.

Short Answer

Expert verified

The required value of $n$ is :- localid="1647799797754" $n = 8$ .

The required value of $r$ is :- localid="1647799803482" $r = 2$ .

Step by step solution

Step 1. Given Information

We have given the following system of equations :-

$\{\begin{cases} n + r = 10 \\ 6 n + 3 r = 54 \end{cases}$

We have to find the values of $n$ and $r$ . We will apply elimination method to solve the system.

Step 2. Eliminate one variable

The given system of equations is :-

$\{\begin{cases} n + r = 10 \\ 6 n + 3 r = 54 \end{cases}$

Now to eliminate one variable $r$ , multiply first equation with $3$ , then we have :-

$\{\begin{cases} 3 (n + r = 10) \\ 6 n + 3 r = 54 \end{cases}$

Simplify the equations :-

$\{\begin{cases} 3 n + 3 r = 30 \\ 6 n + 3 r = 54 \end{cases}$

Sub tract first equation from second equation, then we have :-

$6 n - 6 n = 54 - 30 \Rightarrow 3 n = 24$

Simplify the equation :-

$3 n = 24 \Rightarrow n = \frac{24}{3} \Rightarrow n = 8$

This is the required value of $n$ .

Step 3. Find value of r

Put $n = 8$ , in the first equation $n + r = 10$ , then we have :-

localid="1647799831743" $8 + r = 10$ .

Simplify the equation :-

localid="1647799842079" $8 + r = 10 \Rightarrow r = 10 - 8 \Rightarrow r = 2$

This is the required value of $r$ .

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Eliminate one variable

Step 3. Find value of r

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