Question

Two teachers purchase supplies for their classrooms.

Mr. Bowden purchases 18 journals and 40 pencils for $95.42.
Ms. Jacinto purchases 11 journals and 16 pencils for $53.33.
Each journal costs the same, and each pencil costs the same.

Answer 1

Cost of One Journal = $3.99

Cost of One pen = $0.59

Explanation:

Let

Cost of One Journal = x

Cost of One pen = y

We can make equation from given statements.

Mr. Bowden purchases 18 journals and 40 pencils for $95.42.

`18x+40y=95.42`

Ms. Jacinto purchases 11 journals and 16 pencils for $53.33.

`11x+16y=53.33`

Now solving these equations to find the value of x

`18x+40y=95.42--eq(1)\\11x+16y=53.33--eq(2)`

Multiply eq(1) with 2 and eq(2) with 5

`36x+80y=190.84\\55x+80y=266.65\\-\:\:\:\:-\:\:\:\;\:\:\:\:\:\:\:-\\---------\\-19x=-75.81\\x=(-75.81)/(-19)\\x=3.99\\`

We get the value of x is: x=3.99

Now, putting value of x in equation 1 to find value of y.

`18x+40y=95.42\\18(3.99)+40y=95.42\\71.82+40y=95.42\\40y=95.42-71.82\\40y=23.6\\y=(23.6)/(40)\\y= 0.59`

So, we get the value of y: y = 0.59

Now, finding the costs:

Cost of One Journal = x = $3.99

Cost of One pen = y = $0.59