If x dozen kumquats sell for y dollars, write a formula for the cost of exactly z kumquats. Check your formula by plugging in some easy numbers.
Algebra I
Mrs. McGillicuddy’s Age
How old will Mrs. McGillicuddy be b years from now if she was x years old c years ago?
Babysitting Awake/Asleep
Holly used to get $2.00 per hour babysitting one child if it was awake and $1.50 per hour if it was asleep. Each additional child was another dollar per hour, awake or asleep. If she took care of n children for x hours before bedtime and y hours after bedtime, how much money did she earn? (The answer is a formula.)
Ball-Point Pens on Sale
A certain make of ball-point pen was priced at 50¢ at Chuck’s Bargain Bin, but nobody was buying it. Chuck reduced the price by putting the pens on sale, and then all the remaining pens sold for a total of $31.93. What was the sale price of a pen?
Motorists’ Speeds
Two motorists set out at the same time to go from Toledo to Ft. Wayne, a distance of 100 miles. They both followed the same route and traveled at different, though uniform, speeds of an integral number of miles per hour. The difference in their speeds was a prime number of miles per hour. After they had been driving for two hours, the distance of the slower car from Toledo was five times the distance of the faster car from Ft. Wayne. How fast did the two motorists drive?
Pickanumba, Result is 2
Think of any number, multiply it by 2, then add 4, multiply by 3, divide by 6, subtract the number you started with, and the result will be 2. Explain with algebra why this works.
Curb at Olympic
Some years back, a budget of $25,000 was available to construct 5000 feet of curbing along the road entering Olympic state park. It was desirable to have the maximum possible amount of the more attractive rock curbing and to have the remainder be asphalt diking. At that time, rock curbing cost $6.15 per linear foot and asphalt diking cost $4.30 per linear foot. How much rock curbing could be installed? (Round answer to the nearest foot.)
Sheriff Election
Art, Bruce, and Charlie were running for sheriff. In the election, a total of 15,424 votes were cast. Art received 1006 more than Bruce and 1213 more than Charlie. How many votes did each candidate receive?
Apollo Ticket Prices
For a special show, the Grand Apollo Theater charged ticket prices as follows: adults, $10; students, $3; and children under 12, 50 cents. The theater collected a total of $100 from an audience of 100 people. How many adults, students, and children were in the audience?
Brick on 2-Pan Scale
In demonstrating how a 2-pan scale works, we notice that a brick placed on one side exactly balances 3/4 of a kg plus 3/4 of a brick on the other side. If this is so, what does the brick weigh?