### 8.5 Other Problems

Problem #

Problem Statement

Problems Similar To

1.

10 times a certain number is 3 more than 3 times another number. The sum of the first number and 9 times the second number is 84. Find the numbers.

\begin{equation}10x=3y+3\textrm{ },\textrm{ }x+9y=84\end{equation}

2.

The sum of a number and 2 times another number is 17. The first number is -4 more than the second number. What are the numbers?

\begin{equation}x+2y=17\textrm{ },\textrm{ }x=y-4\end{equation}

3.

Sabina and Lou are reading the same book. Sabina reads 2 pages a day. She had read 9 pages when Lou started reading the book, and Lou reads at a pace of 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?

\begin{equation}y=9+2x\textrm{ },\textrm{ }y=3x\end{equation}

4.

The Acme Transportation company owns 5 times as many mini-buses as regular buses. There are 36 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=5y\textrm{ },\textrm{ }x=y+36\end{equation}

5.

Bob is 16/5 years older than Fred. Fred is 1/5 as old as Bob. How old are they?

\begin{equation}x=y+\frac{16}{5}\textrm{ },\textrm{ }y=\frac{x}{5}\end{equation}

6.

Computer Information Inc. charges $\$49.6$per month plus$\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$53$per month plus$\$0.7$ per minute. For how many minutes of use will the charges the same and how much will those charges be?

\begin{equation}x=49.6+0.2y\textrm{ },\textrm{ }x=53+0.7y\end{equation}

7.

The length of a rectangle is 6cm more than its width. The perimeter of the rectangle is 48cm. What are the rectangle's dimensions?

\begin{equation}x=y+6\textrm{ },\textrm{ }2(x+y)=48\end{equation}

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 10 suits and 5 pair of shoes, Carla has earned $\$85$in commission. For selling 3 suits and 7 pairs of shoes, Benicio has earned$\$42$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}10x+5y=85\textrm{ },\textrm{ }3x+7y=42\end{equation}

9.

Briana's family spend $\$24$on 7 adult tickets and 5 youth tickets at an amusement park. Max's family spent$\$12$ on 3 adult tickets and 3 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}7x+5y=24\textrm{ },\textrm{ }3x+3y=12\end{equation}

10.

Carl bought 8 apples of two different varieties to make a pie. The total cost of the apples was $\$48$. Granny Smith apples cost$\$5$ each and Gala apples cost $\$7\$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=8\textrm{ },\textrm{ }5x+7y=48\end{equation}