Question

A science teacher ordered S2278 worth of microscopes and dissection kits for the new science lab. A total of

26 microscopes and 56 dissection kits were ordered. A microscope costs three 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

`26M + 56D = 2278` ---- equation 1

`M = 3D` ---- equation 2

A microscope costs S51 and a dissection kit costs S17

Explanation:

Given

Represent microscope with M and Dissection kits with D

Cost:

`M = 3D`

`Total = 2278`

Required

Represent as an equation:

To do this, we represent the equation in terms of cost and quantity

In terms of cost, we have:

`26M + 56D = 2278` ---- equation 1

and

`M = 3D` ---- equation 2

Substitute 3D for M in equation 1

`26*3D + 56D = 2278`

`78D + 56D = 2278`

`134D = 2278`

Divide both sides by 134

`D = (2278)/(134)`

`D = 17`

Substitute 17 for D in
`M = 3D`

`M = 3 * 17`

`M = 51`

Hence:

A microscope costs S51 and a dissection kit costs S17