### 8.5 Other Problems

Problem #

Problem Statement

Problems Similar To

1.

73/6 times a certain number is 3 more than 10 times another number. The sum of the first number and 3 times the second number is 27. Find the numbers.

$$\frac{73}{6} \times x=10y+3\textrm{ },\textrm{ }x+3y=27$$

2.

The sum of a number and 5 times another number is 53. The first number is -1 more than the second number. What are the numbers?

$$x+5y=53\textrm{ },\textrm{ }x=y-1$$

3.

Sabina and Lou are reading the same book. Sabina reads 7 pages a day. She had read 7 pages when Lou started reading the book, and Lou reads at a pace of 77/10 pages per day. If their reading rates continue, on which day will Sabina and Lou be reading the same page and which page will that be?

$$y=7+7x\textrm{ },\textrm{ }y=\frac{77}{10} \times x$$

4.

The Acme Transportation company owns 7 times as many mini-buses as regular buses. There are 48 more mini-buses than regular buses. How many of each does Acme own?

$$x=7y\textrm{ },\textrm{ }x=y+48$$

5.

Bob is 60/7 years older than Fred. Fred is 1/7 as old as Bob. How old are they?

$$x=y+\frac{60}{7}\textrm{ },\textrm{ }y=\frac{x}{7}$$

6.

Computer Information Inc. charges $\$46.7$per month plus$\$0.3$ per minute for computer access to its information. Data Access Corporation charges $\$48$per month plus$\$0.8$ per minute. For how many minutes of use will the charges the same and how much will those charges be?

$$x=46.7+0.3y\textrm{ },\textrm{ }x=48+0.8y$$

7.

The length of a rectangle is 8cm more than its width. The perimeter of the rectangle is 40cm. What are the rectangle's dimensions?

$$x=y+8\textrm{ },\textrm{ }2(x+y)=40$$

8.

Carla and Benicio work in a men's clothing store. They earn commission from each suit and each pair of shoes they sell. For selling 3 suits and 2 pair of shoes, Carla has earned $\$28$in commission. For selling 6 suits and 9 pairs of shoes, Benicio has earned$\$96$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

$$3x+2y=28\textrm{ },\textrm{ }6x+9y=96$$

9.

Briana's family spend $\$47$on 5 adult tickets and 6 youth tickets at an amusement park. Max's family spent$\$22$ on 2 adult tickets and 4 youth tickets. What is the price of an adult and a youth ticket?

$$5x+6y=47\textrm{ },\textrm{ }2x+4y=22$$

10.

Carl bought 15 apples of two different varieties to make a pie. The total cost of the apples was $\$65$. Granny Smith apples cost$\$5$ each and Gala apples cost $\$3\$ each. How many of each type of apple did Carl buy?

$$x+y=15\textrm{ },\textrm{ }5x+3y=65$$