A forest inhabited only by borogoves and mome raths contains eighty-two creatures. Borogoves are two-legged animals, while a mome rath has four legs. If the forest contains a total of 234 legs, how many borogoves and how many mome raths live in the forest?
Answer
47 borogoves and 35 mome raths
Example 2
Solve the following word problem:
Blue beads cost $0.50 per ounce and green beads cost $0.75 per ounce. Janine wants to mix blue and green beads to get 10 ounces of a bead mixture worth $0.55 per ounce. How many ounces of each color does Janine need to buy?
Hint
How much will the full 10 ounces of bead mixture cost all together?
Answer
8 oz blue beads and 2 oz green beads
Example 3
Solve the following word problem:
Ayako spent $7.80 on equal weights of white and red beads. The red beads cost twice as much per ounce as the white beads. How much did Ayako spend on each color of beads?
Answer
$2.60 on white beads and $5.20 on red beads
Example 4
Solve the following word problem:
A rectangle has perimeter 18. If each side of the rectangle is doubled, the perimeter of the new rectangle is 36. What were the dimensions of the original rectangle?
Answer
There are infinitely many such rectangles, because the system of equations is dependent.
Example 5
Solve the following word problem:
Jemima wants to make chocolate-chip walnut brownies. Chocolate chips come in a 12oz bag that costs $3. Walnuts come in a 4oz bag that costs $2. If Jemima needs three pounds of chocolate chips and walnuts combined, and has $15 to spend, how many bags of each can she buy?