Name: Date:
Math – Integrated Algebra Ch #3 Review
1. Bray is six years younger than Dan. The sum of their ages is 4. How old are Bray and Dan?
Let x = Dan’s age x + x − 6 = 4
Let x − 6 = Bray’s age 2x – 6 = 4 * No solution
2x = 10
x = 5
x – 6 = −1
Solve for the variable indicated. State any restrictions on possible values of the variables.
2. P = 2L + 2W for W 3. E = for v
where m ≠ 0
Directions. Solve each equation. Check one of them.
4. –7(1 – 4m) = 13(2m – 3) 5. –5(15y – 1) = 2(7y – 16) – y
m = −16 m = = 0.42045
6. (9t + 3) = (15t – 25) + t t = 6
Directions: Solve the problem by defining a variable, writing an equation and solving it.
7. The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first side. The perimeter is 80cm. Find the length of each side.
Let x = The length of the 2nd side x + 2x – 7 + 2x – 3 = 80
Let 2x – 7 = the length of the 1st side 5x – 10 = 80 * The lengths of the Let 2x − 7 + 4 5x = 90 sides are 18 cm, 29
2x − 3 = the length of the 3rd side x = 18 cm, and 33 cm.
2x – 7 = 29
2x – 3 = 33
8. Jack is 14 years younger than Mr. Clemmons. Ten years ago, Mr. Clemmons was three times as old as Jack was then. How old is each now.
Let x = Mr. Clemmons age x – 10 = 3(x − 14 − 10)
Let x − 14 = Jack’s age x – 10 = 3(x − 24) * Mr. Clemmons is 31 and
x – 10 = 3x – 72 Jack is 17.
−2x = − 62
x = 31
x – 14 = 17
9. Robert has two summer jobs. At one job Robert works 30 hours a week and earns $7.83 an hour. At the second job he earns $5.27 an hour and can work as much as he wants. How many hours does Robert need to work at his second job to earn $303.41 a week?
Let x = The # of hours on the second job 7.83(30) + 5.27x = 303.41
234.90 + 5.27x = 303.41 * He must work for
5.27x = 68.51 13 hours.
x = 13
10. Elaine won the track meet with an average speed of 5.1 meters per second. The second place runner had an average speed of 4.8 meters per second. If Elaine finished 3.4 seconds ahead of the second place runner, how long did it take her to cross the finish line?
Let t = Elaine’s time 5.1t = 4.8(t + 3.4)
5.1t = 4.8t + 16.32 * Elaine finished in 54.4
0.3t = 16.32 seconds.
t = 54.4
11. Mikael rides his bike from Unionville to Mount Hope traveling an average of 65 mph. At the same time JT leaves Mount Hope for Unionville traveling at 45 mph. If it is 440 miles between Mount Hope and Unionville, how long before the two guys meet, assuming that each maintains its average speed?
Let t = time it takes to meet 440 = 65t + 45t
440 = 110t * It will take 4 hours.
4 = t
12. Currently, Michael has $60 and his friend Dan has $135. Michael decides to save $5 of his allowance each week. However, Dan decides to spend his whole allowance plus $10 of savings each week. How long will it be before Michael has as much money as Dan?
Let x = # of weeks to have the same 60 + 5x = 135 – 10x
amount of money 15x = 75 * It will take 5 weeks.
x = 5
13. A bottle-nosed whale can dive 440 feet per minute. Suppose a bottle nosed whale is 500 feet deep and dives at this rate. Write and solve an equation to find how long it will take to reach a depth of 2975 feet. Round to the nearest whole minute.
Let x = # of minutes to reach depth 440x + 500 = 2975
440x = 2475 * It will take about 6
x = 5.625 minutes.
14. At Minisink Valley Middle School, 579 students take Spanish. This number has been increasing at a rate of 30 students per year. The number of students taking French is 217 and has been decreasing at a rate of 2 students per year. At these rates when will there be three times as many students taking Spanish as taking French.
Let x = the number of years 579 + 30x = 3(217 – 2x)
579 + 30x = 651 – 6x * It will take two years.
36x = 72
x = 2
15. A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second) but can only sustain this speed for about 20 seconds before it is worn out. While Heidi can only run at 3 feet per second, she can maintain that speed all day long.
a. How far away from the cheetah does the gazelle need to stay for it to be safe?
Let x = the distance from the cheetah 88(20) = 73(20) + x
1760 = 1460 + x * The gazelle must stay
300 = x more than 300 feet away.
b. How far away from the cheetah does Heidi need to stay for her to be safe?
Let x = the distance from the cheetah 88(20) = 3(20) + x
1760 = 60 + x * Heidi must stay more
1700 = x than 1,700 feet away.