Question

Becky purchases choice birdseed for $1.51 per pound and garden birdseed for $0.91 per pound. If they wish to purchase 20 pounds and spend $26 on birdseed, how many pounds of each type should they buy

Answer 1

Cost of each pound choice birdseed = $1.51

Cost of each pound garden birdseed = $0.91

• Let "x" be the amount (in lb) of choice birdseed, and

,

• Let "y" be the amount (in lb) of garden birdseed

Becky purchases 20 pounds of birdseed, so we can write:

$x+y=20$

Total amount spent on birdseeds is $26. Thus, we can write:

$1.51x+0.91y=26$

We can solve for "x" in the first equation, substitute into the second equation and solve for "y". All the steps are shown below:

$\begin{gathered} x+y=20 \\ 1.51x+0.91y=26 \\ ------------- \\ x=20-y \\ So, \\ 1.51(20-y)+0.91y=26 \\ 30.2-1.51y+0.91y=26 \\ -0.6y=-4.2 \\ y=\frac{-4.2}{-0.6} \\ y=7 \end{gathered}$

We can use this value and substitute into the first equation and figure out the value of "x". Shown below:

$\begin{gathered} x+y=20 \\ x+7=20 \\ x=20-7 \\ x=13 \end{gathered}$Answer

Pounds of Choice Birdseeds = 13

Pounds of Garden Birdseeds = 7