Word Problems
One number is nine more than another number. If the sum of the numbers is 65, find both numbers. (Answer must include both an equation representing the original problem and the numbers.)
x + x + 9 = 65
The numbers are 28 and 37.
7x - 6 = -90
x = -12
6m - 17 = 8m - 31
m = 7
Which numbers are solutions to this inequality?
-4x - 19 > 33
-15, -14, -13, -12, -11, -10
-14 and -15
Fourteen, subtracted from a number, divided by 3, equals -8.
Equation only
(n - 14) / 3 = -8
The sum of two numbers is 146. The larger number is sixteen less than five times the smaller. Find both numbers.
Answer must include both equation and numbers.
x + 5x - 16 = 146
The numbers are 27 and 119
(k-7) / -0.4 = 85
k = -27
12 - (3r + 2) = -7(r + 6)
r = -13
-8(13.4 + 7.6) > a
a < -168
The quotient of a number and 0.8, decreased by 11, is 31
Equation only
( n / 0.8 ) - 11 = 31
Lynn put 3 7/8 gallons of gas in her gas tank. If there are now 18 1/6 gallons in the tank, how many gallons did she start with?
x + 3 7/8 = 18 1/6
14 7/24 gallons
-2(2w - 9) = -38
w = 14
-3(n - 5) = 3(n - 9)
n = 7
- 2 7/8 > 1/5(5/8 - t)
t > 15
Sam is an accountant. He finds that he spends two-fifths of his day answering emails. If he spent 3.6 hours answering emails yesterday, how many hours did he work?
Let statement, equation and answer
let h = hours worked
2/5 h = 3.6
h = 9 hours
Sean and Evan are selling rolls of wrapping paper to raise money for new football uniforms. Evan has sold seven more than one-half the number of rolls that Sean has. If they have sold a total of 121 rolls, how many has Evan sold?
Define a variable, write an equation and answer the question
let x = Sean's sales
x + 0.5x + 7 = 121
x = 76
Evan has sold 46 rolls.
93 = 5 - 2(p - 8) - 4p
p = -12
1/4 (20 - 4x) = 6 - x
no solution
4(x+2) = 14 - 2(3 - 2x)
infinitely many solutions
The Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel. If their combined height is 361 feet, how tall is the Gardenview hotel?
Let statement, equation and answer
let p = plaza hotel height
p + 2p - 17 = 361
p = 126.
The Gardenview hotel is 235 feet tall.
Runner A gets a 20 meter head start in a race, and runs at a constant speed of 2.9 meters per second. Runner B runs at a constant speed of 3.4 meters per second. Will Runner B ever catch up to Runner A? If so, after how many seconds?
Write an equation and solve it.
x = 40 seconds
yes at 40 seconds.
1 4/5 = 8m + 4 1/5 - 3m - 7 2/5
m = 1
4a2 + 19 = 68
a = + or - 7/2
The parking meter charges $2 for the first hour, then $0.75 cents per hour thereafter. Nate only has $5. How many hours can he park?
let h = hours
2 + 0.75h <= 5
h <= 4 hours
He can park at most 4 hours
Three-eighths of the 7th grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many total 7th grade students are there?
Let statement, equation and answer.
let s = 7th graders
3/8 x - 7= 140
x = 392