Algebra-1 Problems

8.5 Other Problems


Problem #

Problem Statement

Problems Similar To

1.

7/2 times a certain number is 3 more than 4 times another number. The sum of the first number and 8 times the second number is 74. Find the numbers.

\begin{equation}\frac{7}{2} \times x=4y+3\textrm{ },\textrm{ }x+8y=74\end{equation}

2.

The sum of a number and 4 times another number is 23. The first number is -2 more than the second number. What are the numbers?

\begin{equation}x+4y=23\textrm{ },\textrm{ }x=y-2\end{equation}

3.

Sabina and Lou are reading the same book. Sabina reads 2 pages a day. She had read 5 pages when Lou started reading the book, and Lou reads at a pace of 17/6 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+2x\textrm{ },\textrm{ }y=\frac{17}{6} \times x\end{equation}

4.

The Acme Transportation company owns 8 times as many mini-buses as regular buses. There are 49 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=8y\textrm{ },\textrm{ }x=y+49\end{equation}

5.

Bob is 7 years older than Fred. Fred is 1/8 as old as Bob. How old are they?

\begin{equation}x=y+7\textrm{ },\textrm{ }y=\frac{x}{8}\end{equation}

6.

Computer Information Inc. charges $\$50.6$ per month plus $\$0.3$ per minute for computer access to its information. Data Access Corporation charges $\$59$ 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=50.6+0.3y\textrm{ },\textrm{ }x=59+0.7y\end{equation}

7.

The length of a rectangle is 4cm more than its width. The perimeter of the rectangle is 32cm. What are the rectangle's dimensions?

\begin{equation}x=y+4\textrm{ },\textrm{ }2(x+y)=32\end{equation}

8.

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 3 pair of shoes, Carla has earned $\$39$ in commission. For selling 2 suits and 4 pairs of shoes, Benicio has earned $\$32$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}4x+3y=39\textrm{ },\textrm{ }2x+4y=32\end{equation}

9.

Briana's family spend $\$46$ on 7 adult tickets and 2 youth tickets at an amusement park. Max's family spent $\$89$ on 2 adult tickets and 9 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}7x+2y=46\textrm{ },\textrm{ }2x+9y=89\end{equation}

10.

Carl bought 11 apples of two different varieties to make a pie. The total cost of the apples was $\$27$. Granny Smith apples cost $\$2$ each and Gala apples cost $\$3$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=11\textrm{ },\textrm{ }2x+3y=27\end{equation}