# Open Sentences in Two Variables

• Oct 20th 2008, 10:23 AM
mjp1991
Open Sentences in Two Variables
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. (Hint: The sum of the lengths of any three sides of a quadrilateral must exceed the length of the fourth side.)

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.)

ONLY THE EQUATIONS NEEDED TO SOLVE THESE PROBLEMS ARE NECESSARY.
• Oct 20th 2008, 10:53 AM
masters
Quote:

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.

$50w+100r=500$

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.

$10d+25q=95$

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.)

$3x+y=19$

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.)

$2x+y=15$

ONLY THE EQUATIONS NEEDED TO SOLVE THESE PROBLEMS ARE NECESSARY.

Quote:

Originally Posted by mjp1991
ONLY THE EQUATIONS NEEDED TO SOLVE THESE PROBLEMS ARE NECESSARY.

Sorry about solving the first 2. I didn't see your restriction 'til after