Video solutions to help Grade 7 students learn that any equation can be rewritten to an equivalent equation with expressions that involve only integer coefficients by multiplying both sides by the correct number.

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Common Core For Grade 7

• Students understand and use the addition, subtraction, multiplication, division, and substitution properties of
equality to solve word problems leading to equations of the form px + q = r and p(x + q) = r where p, q,
and r are specific rational numbers.

• Students understand that any equation can be rewritten to an equivalent equation with expressions that
involve only integer coefficients by multiplying both sides by the correct number.

Classwork

Opening Exercise

Every day Heather practices soccer and piano. Each day she practices piano for 2 hours. If after 5 days she practiced both piano and soccer for a total of 20 hours, how many hours, h, per day did Heather practice soccer?

Every day for 5 days, Jake practices soccer. Over the 5 days, he also practices piano for a total of 2 hours. If he practiced piano and soccer for a total of 20 hours, how many hours, h, per day did Jake practice soccer?

Example 1

Fred and Sam are a team in the local 138.2 mile bike-run-athon. Fred will compete in the bike race and Sam will compete in the run. Fred biked at an average speed of 8 miles per hour and Sam ran at an average speed of 4 miles per hour. The bike race began at 6:00 a.m., followed by the run. Sam finished the run at 2:33 a.m. the next morning.

a. How many hours did it take for them to complete the entire bike-run-athon?

b. If is how long it took for Fred to complete the bike race, in hours, write an expression to find Fred’s total distance.

c. Write an expression, in terms of t to express Sam's time.

d. Write an expression, in terms of t, that express Sam's total distance.

e. Write and solve an equation using the total distance both Fred and Sam traveled.

f. How far did Fred bike, and how much time did it take him to complete his leg of the race?

g. How far did Sam, run and how much time did it take him to complete his leg of the race?

Example 2

Shelby is seven times as old as Bonnie. If in 5 years, the sum of Bonnie’s and Shelby’s age is 98, find Bonnie’s present age. Use an algebraic approach.

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