Question

A pet store sells goldfish and hermit crabs,

The store sells 7 goldfish and 3 hermit crabs for $26.

• The store sells 4 goldfish and 5 hermit crabs for $28.

How much would the store sell 6 goldfish and 4 hermit crabs for?

Answer 1

`Cost = \$28`

Explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

`7g + 3h = 26`

The second statement, we have:

`4g + 5h = 28`

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

`7g + 3h = 26` --- (1)

`4g + 5h = 28` --- (2)

Make g the subject in (2)

`4g + 5h = 28`

`4g = 28 - 5h`

Divide both sides by 4

`g = (1)/(4)(28 - 5h)`

Substitute
`(1)/(4)(28 - 5h)` for g in (1)

`7g + 3h = 26`

`7((1)/(4)(28 - 5h)) + 3h = 26`

`(7)/(4)(28 - 5h) + 3h = 26`

Multiply through by 4

`4 * (7)/(4)(28 - 5h) + 4*3h = 26*4`

`7(28 - 5h) + 4*3h = 26*4`

Open bracket

`196 - 35h + 12h = 104`

`196 -23h = 104`

Collect Like Terms

`-23h = 104-196`

`-23h = -92`

Make h the subject

`h = (-92)/(-23)`

`h = (92)/(23)`

`h = 4`

Substitute 4 for h in
`g = (1)/(4)(28 - 5h)`

`g = (1)/(4)(28 - 5*4)`

`g = (1)/(4)(28 - 20)`

`g = (1)/(4)(8)`

`g = 2`

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

`Cost = 6g + 4h`

`Cost = 6*\$2 + 4*\$4`

`Cost = \$12 + \$16`

`Cost = \$28`