Algebra-1 Problems

8.5 Other Problems

Problem #

Problem Statement

Problems Similar To


23/7 times a certain number is 8 more than 3 times another number. The sum of the first number and 3 times the second number is 22. Find the numbers.

\begin{equation}\frac{23}{7} \times x=3y+8\textrm{ },\textrm{ }x+3y=22\end{equation}


The sum of a number and 4 times another number is 22. The first number is 7 more than the second number. What are the numbers?

\begin{equation}x+4y=22\textrm{ },\textrm{ }x=y+7\end{equation}


Sabina and Lou are reading the same book. Sabina reads 9 pages a day. She had read 9 pages when Lou started reading the book, and Lou reads at a pace of 99/10 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?

\begin{equation}y=9+9x\textrm{ },\textrm{ }y=\frac{99}{10} \times x\end{equation}


The Acme Transportation company owns 7 times as many mini-buses as regular buses. There are 24 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=7y\textrm{ },\textrm{ }x=y+24\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 $\$47.4$ per month plus $\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$47$ 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?

\begin{equation}x=47.4+0.2y\textrm{ },\textrm{ }x=47+0.8y\end{equation}


The length of a rectangle is 3cm more than its width. The perimeter of the rectangle is 30cm. What are the rectangle's dimensions?

\begin{equation}x=y+3\textrm{ },\textrm{ }2(x+y)=30\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 4 suits and 9 pair of shoes, Carla has earned $\$77$ in commission. For selling 4 suits and 7 pairs of shoes, Benicio has earned $\$67$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}4x+9y=77\textrm{ },\textrm{ }4x+7y=67\end{equation}


Briana's family spend $\$84$ on 2 adult tickets and 8 youth tickets at an amusement park. Max's family spent $\$180$ on 10 adult tickets and 10 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}2x+8y=84\textrm{ },\textrm{ }10x+10y=180\end{equation}


Carl bought 13 apples of two different varieties to make a pie. The total cost of the apples was $\$34$. Granny Smith apples cost $\$1$ each and Gala apples cost $\$8$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=13\textrm{ },\textrm{ }1x+8y=34\end{equation}