Algebra-1 Problems

8.5 Other Problems


Problem #

Problem Statement

Problems Similar To

1.

73/6 times a certain number is 3 more than 10 times another number. The sum of the first number and 3 times the second number is 27. Find the numbers.

\begin{equation}\frac{73}{6} \times x=10y+3\textrm{ },\textrm{ }x+3y=27\end{equation}

2.

The sum of a number and 5 times another number is 53. The first number is -1 more than the second number. What are the numbers?

\begin{equation}x+5y=53\textrm{ },\textrm{ }x=y-1\end{equation}

3.

Sabina and Lou are reading the same book. Sabina reads 7 pages a day. She had read 7 pages when Lou started reading the book, and Lou reads at a pace of 77/10 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=7+7x\textrm{ },\textrm{ }y=\frac{77}{10} \times x\end{equation}

4.

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}

5.

Bob is 60/7 years older than Fred. Fred is 1/7 as old as Bob. How old are they?

\begin{equation}x=y+\frac{60}{7}\textrm{ },\textrm{ }y=\frac{x}{7}\end{equation}

6.

Computer Information Inc. charges $\$46.7$ per month plus $\$0.3$ per minute for computer access to its information. Data Access Corporation charges $\$48$ 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=46.7+0.3y\textrm{ },\textrm{ }x=48+0.8y\end{equation}

7.

The length of a rectangle is 8cm more than its width. The perimeter of the rectangle is 40cm. What are the rectangle's dimensions?

\begin{equation}x=y+8\textrm{ },\textrm{ }2(x+y)=40\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 3 suits and 2 pair of shoes, Carla has earned $\$28$ in commission. For selling 6 suits and 9 pairs of shoes, Benicio has earned $\$96$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}3x+2y=28\textrm{ },\textrm{ }6x+9y=96\end{equation}

9.

Briana's family spend $\$47$ on 5 adult tickets and 6 youth tickets at an amusement park. Max's family spent $\$22$ on 2 adult tickets and 4 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}5x+6y=47\textrm{ },\textrm{ }2x+4y=22\end{equation}

10.

Carl bought 15 apples of two different varieties to make a pie. The total cost of the apples was $\$65$. Granny Smith apples cost $\$5$ each and Gala apples cost $\$3$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=15\textrm{ },\textrm{ }5x+3y=65\end{equation}