Algebra-1 Problems

8.5 Other Problems

Problem #

Problem Statement

Problems Similar To


10/7 times a certain number is 6 more than 2 times another number. The sum of the first number and 9 times the second number is 25. Find the numbers.

\begin{equation}\frac{10}{7} \times x=2y+6\textrm{ },\textrm{ }x+9y=25\end{equation}


The sum of a number and 7 times another number is 16. The first number is 0 more than the second number. What are the numbers?

\begin{equation}x+7y=16\textrm{ },\textrm{ }x=y+0\end{equation}


Sabina and Lou are reading the same book. Sabina reads 6 pages a day. She had read 5 pages when Lou started reading the book, and Lou reads at a pace of 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=5+6x\textrm{ },\textrm{ }y=7x\end{equation}


The Acme Transportation company owns 4 times as many mini-buses as regular buses. There are 21 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=4y\textrm{ },\textrm{ }x=y+21\end{equation}


Bob is 2 years older than Fred. Fred is 1/3 as old as Bob. How old are they?

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


Computer Information Inc. charges $\$53.3$ per month plus $\$0.3$ per minute for computer access to its information. Data Access Corporation charges $\$54$ 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=53.3+0.3y\textrm{ },\textrm{ }x=54+0.8y\end{equation}


The length of a rectangle is 3cm more than its width. The perimeter of the rectangle is 26cm. What are the rectangle's dimensions?

\begin{equation}x=y+3\textrm{ },\textrm{ }2(x+y)=26\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 9 pair of shoes, Carla has earned $\$99$ in commission. For selling 5 suits and 9 pairs of shoes, Benicio has earned $\$117$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}3x+9y=99\textrm{ },\textrm{ }5x+9y=117\end{equation}


Briana's family spend $\$101$ on 9 adult tickets and 4 youth tickets at an amusement park. Max's family spent $\$94$ on 6 adult tickets and 8 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}9x+4y=101\textrm{ },\textrm{ }6x+8y=94\end{equation}


Carl bought 9 apples of two different varieties to make a pie. The total cost of the apples was $\$29$. 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=9\textrm{ },\textrm{ }3x+4y=29\end{equation}