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=(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