Lesson 6: Percentages and Equations

Percentages and Equations

Student Summary

We can write equations to help us solve percentage problems.

Example: There are 455 students in school today, which is 70% school attendance. How many students go to the school?

The number of students in school today is known in two different ways: as 70% of the students in the school, and also as 455. If $s$ represents the total number of students who go to the school, then 70% of $s$ , or $\frac{70}{100}s$ , represents the number of students that are in school today, which is 455.

We can write and solve the equation:

$\begin{aligned} \frac{70}{100} s &= 455 \\ s &= 455 \div \frac{70}{100} \\ s &= 455 \boldcdot \frac{100}{70}\\ \end{aligned}$

There are 650 students in the school.

$s = 650$

The equation can also be written using the decimal equivalent of $\frac{70}{100}$ , which is 0.7:

$\begin{aligned} 0.7s &= 455 \\ s &= 455 \div 0.7\\ s & = 650 \end{aligned}$

We can check this answer by substituting 650 for $x$ in the equation and seeing if the equation is true.

$\displaystyle \begin{aligned} 0.7x&=455\\0.7(650)&=455\\ 455&=455\end{aligned}$

Visual / Anchor Chart

Standards

Addressing

6.EE.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = q for cases in which p, q, and x are all nonnegative rational numbers.

6.RP.3.c

Use ratio and rate reasoning to solve real-world and mathematical problems.