Percentages and Equations

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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 ss represents the total number of students who go to the school, then 70% of ss, or 70100s\frac{70}{100}s, represents the number of students that are in school today, which is 455.

We can write and solve the equation:

70100s=455s=455÷70100s=455⋅10070\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=650s = 650

The equation can also be written using the decimal equivalent of 70100\frac{70}{100}, which is 0.7:

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

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

0.7x=4550.7(650)=455455=455\displaystyle \begin{aligned} 0.7x&=455\\0.7(650)&=455\\ 455&=455\end{aligned}

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Standards

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6.EE.6

6.EE.7

6.EE.B.6

6.EE.B.7

6.RP.3.c

6.RP.A.3.c