WP10a
Practice - Creating Two Equations
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. Two basketball players, A and B, score half the team's total of 80 points. A scores 6 more points than B. How many points does each one score?
2. The number of men in a class is one less than three times the number of women. There are 40 people in the class. How many are men, and how many are women?
3. Employees A and B earn $4680 per month together. A earns $520 more than B. How much does A earn?
4. A roll of quarters is worth $25. A roll of dimes is worth $5. You have 11 rolls, which are worth $90. How many rolls of each kind do you have?
5. Three people A, B and C work with you. A has worked with you 8 years longer than B. B has worked with you half as long as C. C has worked with you for 10 years. How many years has A worked with you?
6. You are in sales. Your monthly quota is $10,000. During the first week of a particular month, your sales are $2000. During the second week, your sales are twice that. How much do you have to sell during the rest of the month to meet your quota?
7. A rectangle's area is 16 and its length is four times its width. What is its width?
ANSWERS
1. The first equation is A + B = 80/2 = 40. The second equation is A = B + 6. Substitute the second equation into the first to get B + 6 + B = 40. So 2B = 40 - 6 = 34, so B = 17 points and A = 23 points. To check, see that 17 + 23 = 40 and that 23 - 17 = 6.
2. Let m equal the number of men, and w equal the number of women. So m plus w equals 39 (the first equation) and m equals 3w minus 1 (the second equation. Solve the two equations (with two unknowns) by substitution. w = 39 - m. So m = 3(39 - m) -1. m= (117 - 3m) - 1 = 116 - 4m. So 3m = 116, and m = 29. Therefore w = 10. 20 men and 10 women.
3. Let a = the monthly salary of A and let b = the monthly salary of b. We know that a + b = $4680. We also know that a = b + $520. Therefore b = a - $520. Substitute this into the first equation to get a + (a - $520) = $4680, so 2a - $520 = $4680, 2a = $4680 + $520 = $5200, so a = $5200/2 = $2600. Check to be sure that b = $2600 - $520 = $2080, and that $2600 + $2080 = $4680.
4. Let q = the number of rolls of quarters, and let d = the number of rolls of dimes. You know that q + d = 11. You also know that 25q + 5d = 90. Solve by substitution, putting d = 11 - q into the second equation. The answer is that you have 9 rolls of quarters and 2 rolls of dimes.
5. Set up two equations: A = B + 8 and B = C/2. You know that C = 10, so B = C/2 = 5. Substitute B into the first equation to get A = 5 + 8 = 13. A has worked with you for 13 years.
6. Let q be your monthly quota. Let a be your sales in the first week Let b be your sales in the second week. Let d be the difference you have to sell during the rest of the month. You know that d = q - a - b. You know that b = 2a = $4000. Substitute this value for b, $4000, into the first equation to get d = $10,000 - $2000 - $4000 = $6000.
7. A = LW = 16. L = 4W. Substituting the second equation into the first gives A = 4W². Therefore W² = 4 and W=2.