Word Problems involving Linear Equations of One Variable

As you solve the following word problems be sure to declare your variable and any other unknowns before writing your equation and solving. Please show your work on a separate piece of paper for credit.

1.) The 5th Avenue Bridge is 80 feet shorter than the Broadway Bridge. The sum of the lengths of the two bridges is 1704 feet. How long is each bridge?

2.) The perimeter of a rectangle is 76in. The length is two more than twice the width. Find the dimensions.

3.) A triangle has a perimeter of 53 in. The shortest side of the triangle is two more than one -third of the longest side. The other side is five less than the longest side. Find the dimensions.

4.) Alex spent $3,100 more on his car than Bailee did. Elyse spent $675 less than Bailee spent on her car. Altogether, the three spent $31,501. How much did each spend on their cars?

5.) The sum of three consecutive integers is equal to seventy-eight. Find the integers.

6.) Two houses on the same side of the street have house numbers that are consecutive odd integers. If the sum of the two house numbers is 5228, what are the two house numbers?

7.) Find two consecutive even integers if their sum is 86.

8.) The sum of two consecutive integers is equal to the sum of half of the smaller number and sixteen . Find the two numbers.

9.) Tom pays $2 every time he places an overseas call plus 7 cents per minute. If he spends $3.61 on a call to Italy, how long was he on the phone?

10.) Michael gets a $8 commission for each warranty plan that he sells, and $.50 for each e-mail address he gets from the customer. If he makes a total of $50 in one shift, and sells or collects 40 items, how many of each did he sell?

11.) Sydney’s parents pay her according to her grades. For each “A” that she earns, they add $12 and for each “C” they subtract $5 dollars. On a recent grade period, she got only “A’s” and “C’s” for her 6 classes. If she got a total of $21, how many of each grade did she get?

12.) Kira bought some 2-liter bottles of soda for $1.75 each for her party. She also bought some bags of potato chips for $3.25 each. If she spent $36.75 and bought 15 items, how many of each did she buy?

13.) A theater charges $9.75 for each evening shows and $7 for matinees. If they take in a total of 2300 tickets and had total receipts of $20,973, how many of each type of ticket did they sell?

14.) Kristina makes $8.50 per hour. She makes double time for every hour that she works on Saturday. If she works forty hours during the week and earns $425, how many hours did she work on Saturday?

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