The good ship Gemini is twice as old as its boiler was when the ship was as old as the boiler is now. If the sum of their ages is 49 years, how old is the ship? How old is the boiler?
Sophia buys jellybeans at 5 for 3 cents, and sells them at 6 for 5 cents. How many must she sell in order to make a profit of $3.50?
A woman divided $1 among 12 children. Boys got 7 cents; girls got 9 cents. How many girls were there?
Five racing cars are tearing along on a figure-8 track that has a total length of 7 miles. The cars A, B, C, D, and E have speeds, respectively, of 60, 72, 75, 80, and 96 mph. High walls are located along each side of the track; and so, should any two cars meet at the center, they will collide. Each driver is wondering, “How did I get myself into this? Who is Stella?” If the cars started at the center, all going the same way, will two cars eventually collide? If so, which two, and after how many miles and how many minutes?
A large, beautifully-kept rectangular lawn 40 feet by 60 feet is crossed by four straight paths as shown. The paths are all the same width. If the total area of the paths is 736 square feet, how wide is each path?
Harry’s Rent-a-Heap will rent you a rusted 1968 Ford van for $15 per day plus
$ .20 per mile.
- How much will you pay if you rent the van for 3 days and drive it 245 miles?
- How much will you pay if you rent it for d days and drive it m miles? (The answer is a formula.)
On a special day at the West Side Market, the grapefruit are arranged in a compact stack of filled-in equilateral triangles with 14 grapefruit on each edge of the bottom triangle, 13 on each edge of the one above, and so on all the way up to the top where there is 1 graperfruit sitting all alone. How many grapefruit are in the entire stack?
Liz earned d dollars for h hours of babysitting. At that rate, how much will she earn in x hours? Write a formula that works. Then use numbers to check it: Make up a reasonable hourly rate for babysitting, assume she sits for 3 hours (that’s h), and get her total (that’s d). Now figure out what she’d get for 5 hours (that’s x) and see if your formula works.
Find the pattern for these equations, and then make up one more of your own, using the same pattern.
13 � 62 = 31 � 26