1.

A sofa costs $50 less than three times the cost of a shair. If the sofa and chair together cost $650, how much more does the sofa cost than the chair ?

Answer»

`$175`
`$225`
`$300`
`$475`

Solution :Write a system of equations where c = the cost of the chair in dollars and s = the cost of the SOFA in dollars. A sofa costs `$50` less than THREE times the cost of the chair, or `s =3c-50,` together, a sofa and a chair cost `$650, so s +c= 650.` The system is:
`{{:(s = 3c -50),(s+c=650):}`
The TOP EQUATION is already solved for s, so substitute `3c-50` into the bottom equation for s and solve for c:
`3c-50+c =650`
` 4c-50=650`
`4c =700`
`c = 175`
Remember to check if you solved for the right thing! The chair costs `$175,` so the sofa costs `3 (175)-50=525-50=$475.` This means the sofa costs `$475-$175=$330` more than the chair. Therefore, (C ) is correct.


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