Question

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.

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

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.

4. An isosceles triangle has perimeter 15m. Find all integral possibilities for the lengths of the sides in meters.

Answer 1

In the following problem, (a) choose two variables to represent the numbers asked for, (b) write an open sentence relating the variables, and (c) solve the open sentence and give the answer to the problem. (Include solutions in which one of the variables is zero.)
Luis has 95 cents in dimes = D SAY and quarters = Q SAY. Find all possibilities for the number of each type of coin he could have.
TOTAL NUMBER OF DIMES AND QUARTERS = D+Q
VALUE OF DIMES = D*10=10D CENTS
VALUE OF QUARTERS =Q*25 = 25Q CENTS
TOTAL VALUE = 95 CENTS = 10D+25Q CENTS...
TO SOLVE WE SHOULD HAVE ANOTHER PARAMETER
LET THE TOTAL NUMBER OF COINS = 5
THEN D+Q = 5

D=5-Q
10(5-Q)+25Q=95
50-10Q+25Q=95
15Q=95-50=45
Q=3
D=2 IS ONE SOLUTION SET
IF YOU WANT ALL POSSIBILITIES THEN
Q=1....D=7
Q=3....D=2
THERE IS NO SOLUTION FOR D OR Q = 0 AS PER YOUR GIVEN DATA