Snow Day Work
The ACT is notorious for “abstract problems” Abstract problems are problems that use letters instead of numbers and are solved with letters in your answer rather than numbers. Look at question number 1 as an example. Instead of trying to solve these with letters, I find it easier to turn the problems into “concrete” problems with real numbers. Let’s do this with question number 1. Instead of saying a man’s weekly salary is x dollars, let’s say x = $100 (an easy number I just picked out of the air!) and let’s pretend that he saves $10 instead of y dollars (again, another easy number I randomly picked). To find what part of his salary he spends I would take $100 (what he earns) - $10 (what he spends) to see that he saves $90. Then, to find what part that is, I would take $90 and divide that by the total he had $100 for an answer of 90%. So I took (100 – 10) / 100 . . . OR (x – y) / x. Answer G.
Snow Day #1 Solve problems 1 – 5
Snow Day #2 Solve problems 6 – 10
Snow Day #3 Solve problems 11 - 15
1. If a man’s weekly salary is $x and he saves $y, what part of his weekly salary does he spend?
2. A factory employs m men and w women. What part of its employees are women?
3. If x men can do a job in h days, how long would y men take to do the same job?
4. At c cents per pound, what is the cost of a ounces of candy?
5. If p pencils cost d dollars, how many pencils can be bought for c cents?
6. David had d dollars. After a shopping trip, he returned with c cents. How many CENTS did he spend?
7. How many ounces are there in p pounds and q ounces?
8. How many passengers can be seated on a plane with r rows, if each row consists of d double seats and t triple seats?
9. How many dimes are there in 4x – 1 cents?
10. Joe spent k cents of his allowance and has r cents left. How many dollars was his allowance?
11. If u represents the tens’ digit of a certain number and t represents the units’ digit, then the number with the digits reversed can be represented by:
12. If p pounds of potatoes cost $k, find the cost (in cents) of one pound of potatoes.
13. Mr. Unger rents a car for d days. He pays m dollars per day for each of the first 7 days, and half that rate for each additional day. Find the total charge if d > 7.
14. A salesman earns 90 doallrs per week plus a 4% commission on all sales over $1000. One week he sells $r worth of merchandise (r > 1000). How much money does he earn that week?
15. Elliot’s allowance was just raised to k dollars per week. He gets a raise of c dollars per week every 2 years. How much will his allowance be per week y years from now? (Assume y is an even number.)