### 8.5 Other Problems

Problem #

Problem Statement

Problems Similar To

1.

109/2 times a certain number is 9 more than 10 times another number. The sum of the first number and 2 times the second number is 22. Find the numbers.

$$\frac{109}{2} \times x=10y+9\textrm{ },\textrm{ }x+2y=22$$

2.

The sum of a number and 6 times another number is 46. The first number is 4 more than the second number. What are the numbers?

$$x+6y=46\textrm{ },\textrm{ }x=y+4$$

3.

Sabina and Lou are reading the same book. Sabina reads 8 pages a day. She had read 2 pages when Lou started reading the book, and Lou reads at a pace of 26/3 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?

$$y=2+8x\textrm{ },\textrm{ }y=\frac{26}{3} \times x$$

4.

The Acme Transportation company owns 5 times as many mini-buses as regular buses. There are 40 more mini-buses than regular buses. How many of each does Acme own?

$$x=5y\textrm{ },\textrm{ }x=y+40$$

5.

Bob is 5 years older than Fred. Fred is 1/2 as old as Bob. How old are they?

$$x=y+5\textrm{ },\textrm{ }y=\frac{x}{2}$$

6.

Computer Information Inc. charges $\$46.8$per month plus$\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$45$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?

$$x=46.8+0.2y\textrm{ },\textrm{ }x=45+0.8y$$

7.

The length of a rectangle is 10cm more than its width. The perimeter of the rectangle is 56cm. What are the rectangle's dimensions?

$$x=y+10\textrm{ },\textrm{ }2(x+y)=56$$

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 5 suits and 2 pair of shoes, Carla has earned $\$52$in commission. For selling 6 suits and 6 pairs of shoes, Benicio has earned$\$84$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

$$5x+2y=52\textrm{ },\textrm{ }6x+6y=84$$

9.

Briana's family spend $\$57$on 2 adult tickets and 9 youth tickets at an amusement park. Max's family spent$\$40$ on 5 adult tickets and 2 youth tickets. What is the price of an adult and a youth ticket?

$$2x+9y=57\textrm{ },\textrm{ }5x+2y=40$$

10.

Carl bought 16 apples of two different varieties to make a pie. The total cost of the apples was $\$95$. Granny Smith apples cost$\$2$ each and Gala apples cost $\$9\$ each. How many of each type of apple did Carl buy?

$$x+y=16\textrm{ },\textrm{ }2x+9y=95$$