Algebra 1

Exponents

Linear Equations

WORD PROBLEMS

ALGEBRA 1

MIXED

100

What is the value of

2³x 3²

100

solve

x+2=-3

-5

100

If 1/3 of a number is 4 less than 1/2 of the number, the number is

24. Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.

100

If (2^3)^2 = 4^p, then 3^p =

100

In how many different ways can five students be seated in three chairs?

60. 5x4x3=60

200

What is the value of (1,943,845)⁰

200

solve

2x-1=5

200

Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is

x-25

200

When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?

$120.

200

The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?

$10.00 Because $5 + 0.5($10) = $10.

300

Write in positive exponents.

a^-3

1/a³

300

solve

-3(x-3)=18

-3

300

A boat moored in Richardson Bay (Sausalito) has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?

5 rungs. This number of rungs will be exposed. As the tide comes in, the boat will rise up.

300

Simplify (x + 2)^2 - x^2

4(x+1) Note: x^2 + 4x + 4 - x^2

300

Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?

1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.

400

Simplify

a³x b²x a²x b⁴

a⁵b⁶

400

solve

(-1/3)(-3x+6)=6

400

Jars A, B, and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among the jars so that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1:2:3?

4. Since jars A, B, and C each contain 8 marbles, there are 24 marbles in the three jars. Let x, 2x, and 3x represent the new numbers of marbles in jars A, B, and C, respectively. Hence, x + 2x + 3x = 24 or 6x = 24, so x=4.

400

For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?

400

Five students, all of different heights, are randomly arranged in a line. What is the probability that the tallest student will be first in line and the shortest student will be last in line?

1/20. 1x3x2x1x1=6, 6 ways in which students can be arranged under given conditions. Under no conditions, the ways are 5x4x3x2x1=120. 6/120=1/20.

500

Simplify

(a²b)³/ a⁴b⁵

a²/ b²

500

Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?

2 hours and 40 minutes. If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.

500

Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?

$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.

500

For how many integer values of b is b+3>0 and 1>2b-9?

Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.

500

x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?

32. x=70, y=38. 70-38=32.