Name _______________________
5.5. Solving Two-Step Equations
Write the following two-step equations from verbal models.
1. Two times a number, plus seven, is nineteen.
2. Three times a number, plus five, is twenty.
3. Six times a number, added to ten, is forty-six.
4. Seven less than two times a number is twenty-one.
5. Eight less than three times a number is sixteen.
6. A number divided by two, plus seven, is ten.
7. A number divided by three and then combined with six is eleven.
8. Two less than a number divided by four is ten.
Solve each two-step equation for the unknown variable.
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Write an expression and/or solve each problem.
21. Augusta sells t-shirts at the school store. On Tuesday, Augusta sold seven less than twice the number of t-shirts she sold on Monday. She sold three t-shirts on Tuesday. Write an algebraic equation to represent , the number of t-shirts August sold on Monday.
22. There are 19 green marbles in a box. The number of green marbles in the box is six more than half the number of red marbles in the box. Write an algebraic equation to represent , the number of red marbles in the box.
23. For each babysitting job he takes on, Manuel charges $2 for bus fare plus an additional $6 for each hour he works at the job. On Saturday, Manuel earned $26 for one babysitting job.
a. Write an equation to represent h, the total number of hours that Manuel babysat during his $26 job.
b. Determine the total number of hours that Manuel babysat during that job.
24. Sophia has 29 trading cards in her collection. The number of cards in Sophia's collection is equal to one less than one-third of the number of trading cards in her brother Eli's collection.
a. Write an equation to represent e, the number of trading cards in Eli's collection.
b. Determine the number of trading cards in Eli's collection.