Question

Johnny works at the health food store and is planning to grind a special blend of butter by mixing Peanuts which sells for $3 per pound and almond which sells for 5.50 pounds. how many pounds of each type should she use if she needs 10 pounds of almondpeanut butter which sells for $4.50 a pound ?

Answer 1

Let x be the number of peanuts pounds and y be the number of almod pounds. Then, we can write

$3x+5.50y=4.50(10)$

and

$x+y=10$

Then, we have 2 equations in 2 unknowns. By multipliying by -3 the secon equation, we have an equivalent system of equations:

$\begin{gathered} 3x+5.50y=45 \\ -3x-3y=-30 \end{gathered}$

so, by adding both equations, we get

$2.5y=15$

which gives

$\begin{gathered} y=\frac{15}{2.5} \\ y=6 \end{gathered}$

Then, by substituting this result into the equation x+y=10, we obtain

$x+6=10$

which gives

$\begin{gathered} x=10-6 \\ x=4 \end{gathered}$

Therefore, she needs 4 pounds of peanuts and 6 pound of almonds