Algebra-1 Problems

8.5 Other Problems

Problem #

Problem Statement

Problems Similar To


26/3 times a certain number is 8 more than 10 times another number. The sum of the first number and 5 times the second number is 44. Find the numbers.

\begin{equation}\frac{26}{3} \times x=10y+8\textrm{ },\textrm{ }x+5y=44\end{equation}


The sum of a number and 7 times another number is 70. The first number is -2 more than the second number. What are the numbers?

\begin{equation}x+7y=70\textrm{ },\textrm{ }x=y-2\end{equation}


Sabina and Lou are reading the same book. Sabina reads 8 pages a day. She had read 3 pages when Lou started reading the book, and Lou reads at a pace of 9 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=3+8x\textrm{ },\textrm{ }y=9x\end{equation}


The Acme Transportation company owns 8 times as many mini-buses as regular buses. There are 70 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=8y\textrm{ },\textrm{ }x=y+70\end{equation}


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

\begin{equation}x=y+1\textrm{ },\textrm{ }y=\frac{x}{2}\end{equation}


Computer Information Inc. charges $\$57$ per month plus $\$0.3$ per minute for computer access to its information. Data Access Corporation charges $\$59$ 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=57+0.3y\textrm{ },\textrm{ }x=59+0.8y\end{equation}


The length of a rectangle is 4cm more than its width. The perimeter of the rectangle is 40cm. What are the rectangle's dimensions?

\begin{equation}x=y+4\textrm{ },\textrm{ }2(x+y)=40\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 3 suits and 5 pair of shoes, Carla has earned $\$34$ in commission. For selling 6 suits and 5 pairs of shoes, Benicio has earned $\$58$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}3x+5y=34\textrm{ },\textrm{ }6x+5y=58\end{equation}


Briana's family spend $\$102$ on 9 adult tickets and 6 youth tickets at an amusement park. Max's family spent $\$118$ on 10 adult tickets and 9 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}9x+6y=102\textrm{ },\textrm{ }10x+9y=118\end{equation}


Carl bought 11 apples of two different varieties to make a pie. The total cost of the apples was $\$25$. Granny Smith apples cost $\$1$ each and Gala apples cost $\$3$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=11\textrm{ },\textrm{ }1x+3y=25\end{equation}