3.10: Word Problems
Pocket folders are $0.39 each at a store. If Carolyn paid $7.02, how many did she buy?
Define your variable, set up an equation, and solve.
Let f = folders
0.39f = 7.02
f = 18 folders
One number is 8 less than another number. The total of the two numbers is 78. Find both numbers.
Define your variable, set up an equation, and solve.
Let 1st # = x - 8; Let 2nd # = x
x + x - 8 = 78
x = 43
43, 55
What do we need to watch out for when solving inequalities?
When multiplying or dividing by a negative you have to switch the inequality sign.
Solve: -2(p - 7) < -8
-2p + 14 < -8
-2p < -22
p > 11
Scott takes two-thirds of his body weight and drinks that amount of water in ounces per day. If he drinks 118 ounces each day, what does he weigh?
Define your variable, set up an equation, and solve.
Let w = weight
2/3 w = 118
w = 177 lbs
The sum of two consecutive numbers is 125. Find both numbers.
Define your variable, set up an equation, and solve.
Let 1st # = x; Let 2nd # = x + 1
x + x + 1 = 125
x = 62
62, 63
Graph the inequality: x >= -3
Check graph.
Solve: 29 - 2(3 - 5w) > 13
29 - 6 + 10w > 13
23 + 10w > 13
10w > -10
w > -1
Kate has 79 more envelopes to stamp before she can send off her wedding invitations. If she is sending 234 invitations in all, how many has she stamped so far?
Define your variable, set up an equation, and solve.
Let s = invitations stamped
s + 79 = 234
s = 155 invitations stamped
Ryan has one less than four times the number of songs on his spotify than Olivia. In total, they have 469 songs. How many songs does Olivia have?
Define your variable, set up an equation, and solve.
Let Ryan's songs = 4x - 1; Let Olivia's songs = x
4x - 1 + x = 469
x = 94 songs
Translate and graph the inequality: a number is no more than 9.
n < = 9
Check graph
Solve: 4(3m + 10) > -3m - 51 + 8m
12m + 40 > 5m - 51
7m > -91
m > -13
Driving at an average speed of 52 mph, how long will it take someone to travel 390 miles?
Define your variable, set up an equation, and solve.
Let h = hours
52h = 390
h = 7.5 hours
The sum of three consecutive integers is 39. Find the numbers.
Define your variable, set up an equation, and solve.
Let 1st # = x; Let 2nd # = x + 1; Let 3rd # = x + 2
x + x + 1 + x + 2 = 39
x = 12
12, 13, 14
Solve: 4 - 3k < -23
k > 9
Solve and list 3 numbers that are solutions: 4c - 9 < 6c + 25
4c < 6c + 34
-2c < 34
c > -17
Possible solutions: -5, 0, 10
A plant is 14 inches tall. If it grows 3 inches per year, how many years will it take to reach a height of 38 inches?
Define your variable, set up an equation, and solve.
Let y = years
14 + 3y = 38
y = 8 years
Adalyn has nine more than twice the number of skittles that Morgan has. If twice the number of skittles that Adalyn has is two more than five times the number of skittles that Morgan has, how many does each girl have?
Define your variable, set up an equation, and solve.
Let Adalyn's skittles = 9 + 2s; Let Morgan's skittles = s
2(9 + 2s) = 2 + 5(s)
s = 16
Morgan has 16 skittles, and Adalyn has 41 skittles
Solve: w/-7 + 4 > 5
w < -7
Solve: 0.5(-16x + 2) - 7 > 13x - 6
-8x + 1 - 7 > 13x - 6
-8x - 6 > 13x - 6
-8x > 13x
0 > 21x
0 > x