Some problem situations provide you with an inequality to use in order to solve the problem.
For what values of x will the angle shown below be acute? Acute angles have a measure, m, 0 < m < 90.
Substitute the angle measure, (4x – 1)°, into the given inequality,
0 < m < 90.
Minimum:
0 < 4x – 1
one-fourth 1 4 < x
Maximum:
4x – 1 < 90
x < 22 one-fourth 3 4
Therefore, the values of x which will yield an acute angle are:
one-fourth 1 4 < x < 22 three-fourths 3 4
The student council is raising money for a new mascot uniform by selling homecoming ribbons. They spent $125 on supplies to make the ribbons and charge $1.50 per ribbon they sell. The student council wants to earn a profit of at least $325. The inequality
p ≥ 1.50n – 125, can be used to determine n, the number of ribbons they need to sell to make a profit of p. What is the minimum number of ribbons the student council must sell to meet their goal?
Source: Homecoming mum, Krissa Corbett Cavouras, Flickr
Use the given inequality, p ≥ 1.50n – 125 to determine the number of ribbons needed to sell.
Substitute the goal of $325: 325 ≥ 1.50n – 125
450 ≥ 1.50n
300 ≥ n
Therefore, the student council must sell at least 300 homecoming ribbons to meet their fund raising goal.