Question

A science teacher ordered $3980 worth of microscopes and dissection kits for the new science lab. A total of 38 microscopes and 47 dissection kits were ordered. A microscope costs four times as much as a dissection kit. Write a system of linear equations that represents this situation. What is the cost of each item?

Answer 1

Cost of a kit is $20

cost of a microscope is $80

Explanation:

Here, we want to write a set of equations and solve

Let the cost of a microscope be $m while the cost of a kit be $k

Total cost of 38 microscopes will be 38 * m = $38m

Total cost of 47 kits = 47 * k = $47k

The sum of these is $3980

That will be;

47k + 38m = 3980 ••••••(i)

A microscope cost 4 times a kit

Mathematically;

m = 4k •••••••••(ii)

Substitute ii into i

47k + 38(4k) = 3980

47k + 152k = 3980

199k = 3980

k = 3980/199

k = $20

Recall;

m = 4k

m = 4 * 20 = $80