Question

A shoe company is going to close one of its two stores and combine all the inventory from

both stores. These polynomials represent the inventory in each store:
Store A:
2
늘
0-19-
Store B: 39?-
Which expression represents the combined inventory of the two stores?

Answer 1

`(7)/(2)g^2 -(4)/(5)g+(15)/(4)`

Explanation:

Given

`A:(1)/(2)g^2+(7)/(2)`

`B: 3g^2-(4)/(5)g+(1)/(4)`

Required

Inventory for both stores

We simply add up the given inventories

`A + B =(1)/(2)g^2+(7)/(2) + 3g^2-(4)/(5)g+(1)/(4)`

Collect like terms

`A + B =(1)/(2)g^2+ 3g^2 -(4)/(5)g+(1)/(4)+(7)/(2)`

Take LCM and solve

`A + B =(g^2 + 6g^2)/(2) -(4)/(5)g+(1)/(4)+(7)/(2)`

`A + B =(7)/(2)g^2 -(4)/(5)g+(1)/(4)+(7)/(2)`

`A + B =(7)/(2)g^2 -(4)/(5)g+(1+14)/(4)`

`A + B =(7)/(2)g^2 -(4)/(5)g+(15)/(4)`

Hence, the combined inventory is:
`(7)/(2)g^2 -(4)/(5)g+(15)/(4)`