Algebra-1 Problems

8.5 Other Problems

Problem #

Problem Statement

Problems Similar To


12 times a certain number is 3 more than 9 times another number. The sum of the first number and 4 times the second number is 24. Find the numbers.

\begin{equation}12x=9y+3\textrm{ },\textrm{ }x+4y=24\end{equation}


The sum of a number and 6 times another number is 28. The first number is 0 more than the second number. What are the numbers?

\begin{equation}x+6y=28\textrm{ },\textrm{ }x=y+0\end{equation}


Sabina and Lou are reading the same book. Sabina reads 4 pages a day. She had read 5 pages when Lou started reading the book, and Lou reads at a pace of 29/6 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=5+4x\textrm{ },\textrm{ }y=\frac{29}{6} \times x\end{equation}


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?

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


Bob is 9 years older than Fred. Fred is 1/10 as old as Bob. How old are they?

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


Computer Information Inc. charges $\$51.2$ per month plus $\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$52$ 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=51.2+0.2y\textrm{ },\textrm{ }x=52+0.7y\end{equation}


The length of a rectangle is 10cm more than its width. The perimeter of the rectangle is 28cm. What are the rectangle's dimensions?

\begin{equation}x=y+10\textrm{ },\textrm{ }2(x+y)=28\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 10 suits and 6 pair of shoes, Carla has earned $\$48$ in commission. For selling 6 suits and 6 pairs of shoes, Benicio has earned $\$36$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}10x+6y=48\textrm{ },\textrm{ }6x+6y=36\end{equation}


Briana's family spend $\$38$ on 6 adult tickets and 2 youth tickets at an amusement park. Max's family spent $\$117$ on 9 adult tickets and 9 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}6x+2y=38\textrm{ },\textrm{ }9x+9y=117\end{equation}


Carl bought 11 apples of two different varieties to make a pie. The total cost of the apples was $\$86$. Granny Smith apples cost $\$10$ each and Gala apples cost $\$4$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=11\textrm{ },\textrm{ }10x+4y=86\end{equation}