Algebra-1 Problems

8.5 Other Problems

Problem #

Problem Statement

Problems Similar To


62/9 times a certain number is 6 more than 7 times another number. The sum of the first number and 8 times the second number is 73. Find the numbers.

\begin{equation}\frac{62}{9} \times x=7y+6\textrm{ },\textrm{ }x+8y=73\end{equation}


The sum of a number and 4 times another number is 24. The first number is -1 more than the second number. What are the numbers?

\begin{equation}x+4y=24\textrm{ },\textrm{ }x=y-1\end{equation}


Sabina and Lou are reading the same book. Sabina reads 8 pages a day. She had read 9 pages when Lou started reading the book, and Lou reads at a pace of 65/7 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+8x\textrm{ },\textrm{ }y=\frac{65}{7} \times x\end{equation}


The Acme Transportation company owns 8 times as many mini-buses as regular buses. There are 63 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=8y\textrm{ },\textrm{ }x=y+63\end{equation}


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

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


Computer Information Inc. charges $\$49.8$ per month plus $\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$50$ 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=49.8+0.2y\textrm{ },\textrm{ }x=50+0.7y\end{equation}


The length of a rectangle is 9cm more than its width. The perimeter of the rectangle is 50cm. What are the rectangle's dimensions?

\begin{equation}x=y+9\textrm{ },\textrm{ }2(x+y)=50\end{equation}


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 6 suits and 8 pair of shoes, Carla has earned $\$52$ in commission. For selling 9 suits and 2 pairs of shoes, Benicio has earned $\$28$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}6x+8y=52\textrm{ },\textrm{ }9x+2y=28\end{equation}


Briana's family spend $\$92$ on 8 adult tickets and 10 youth tickets at an amusement park. Max's family spent $\$44$ on 2 adult tickets and 6 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}8x+10y=92\textrm{ },\textrm{ }2x+6y=44\end{equation}


Carl bought 14 apples of two different varieties to make a pie. The total cost of the apples was $\$46$. Granny Smith apples cost $\$3$ each and Gala apples cost $\$4$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=14\textrm{ },\textrm{ }3x+4y=46\end{equation}