Originally Posted by

**mjp1991** 1. Bruce, an appliance salesman, earns a commission of $50 for each washing machine he sells and $100 for each refrigerator. Last month he earned $500 in commissions. Find all possibilities for the number of each kind of appliance he could have sold.

$\displaystyle 50w+100r=500$

Since he cannot sell a fractional appliance, the number of washing machines must be 0, 2, 4, 6, 8, or 10

(w, r) = (0, 5), (2, 4), (4, 3), (6, 2), (8, 1), (10, 0)

2. Luis has 95 cents in dimes and quarters. Find all possibilities for the number of each type of coin he could have.

$\displaystyle 10d+25q=95$

Using similar logic as #1, (d, q) = (2, 3), (7, 1)

3. A certain quadrilateral has three sides of equal length and its perimeter is 19cm. Find all integral possibilities for the lengths of the sides in centimeters. (*Hint:* The sum of the lengths of any three sides of a quadrilateral must exceed the length of the fourth side.)

$\displaystyle 3x+y=19$

4. An isosceles triangle has perimeter 15m. Find all integral possibilities for the lengths of the sides in meters. (*Hint:* The sum of the lengths of any two sides of a triangle must exceed the third side.)

$\displaystyle 2x+y=15$

ONLY THE EQUATIONS NEEDED TO SOLVE THESE PROBLEMS ARE NECESSARY.