Question

In a new development, 50 one and two-bedroom condominiums were sold. Each one-bedroom condominium sold for $120 thousand and each two-bedroom condominium sold for $150 thousand. If sales totaled $7050 thousand, how many of each type of unit was sold?

Answer 1

15,35

Explanation:

Let no. of one bedrooms = x, then no. of two bedrooms = 50 - x.

Cost of x bedrooms @$120 = $120 x

Cost of 50 - x two bedrooms @$150 = $150(50 -x)

Now as per question,

`rArr 120x + 150(50-x) = 7050`

`rArr 120x + 7500 - 150x = 7050`

`rArr -30x = 7050-7500 = -450`

`rArr x = (-450)/-30`

`rArr x = 15`

So, no. of 1 bedrooms = 15 and no. of two bedrooms = 50 - 15 = 35.

Answer 2

In formula (`t`=number of two bedrooms, `s`=one-bedroom):
`120s+150t=7050`

Explanation:

Since `s+t=50->s=50-t`

Now substitute:
`120(50-t)+150t=7050->`
`6000-120t+150t=7050->`
Subtract 6000 from both sides:
`cancel6000-cancel6000-120t+150t=7050-6000->`
`30t=1050->t=1050//30=35->s=50-35=15`

Conclusion : 15 one-bedroom and 35 two-bedroom.

Check : `15xx120+35xx150=7050`. Check!