Algebra-1 Problems

8.5 Other Problems


Problem #

Problem Statement

Problems Similar To

1.

27/4 times a certain number is 9 more than 9 times another number. The sum of the first number and 7 times the second number is 43. Find the numbers.

\begin{equation}\frac{27}{4} \times x=9y+9\textrm{ },\textrm{ }x+7y=43\end{equation}

2.

The sum of a number and 8 times another number is 66. The first number is 3 more than the second number. What are the numbers?

\begin{equation}x+8y=66\textrm{ },\textrm{ }x=y+3\end{equation}

3.

Sabina and Lou are reading the same book. Sabina reads 2 pages a day. She had read 9 pages when Lou started reading the book, and Lou reads at a pace of 19/5 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=9+2x\textrm{ },\textrm{ }y=\frac{19}{5} \times x\end{equation}

4.

The Acme Transportation company owns 10 times as many mini-buses as regular buses. There are 72 more mini-buses than regular buses. How many of each does Acme own?

\begin{equation}x=10y\textrm{ },\textrm{ }x=y+72\end{equation}

5.

Bob is 15/4 years older than Fred. Fred is 1/4 as old as Bob. How old are they?

\begin{equation}x=y+\frac{15}{4}\textrm{ },\textrm{ }y=\frac{x}{4}\end{equation}

6.

Computer Information Inc. charges $\$48.8$ per month plus $\$0.2$ per minute for computer access to its information. Data Access Corporation charges $\$49$ 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=48.8+0.2y\textrm{ },\textrm{ }x=49+0.8y\end{equation}

7.

The length of a rectangle is 4cm more than its width. The perimeter of the rectangle is 36cm. What are the rectangle's dimensions?

\begin{equation}x=y+4\textrm{ },\textrm{ }2(x+y)=36\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 10 suits and 3 pair of shoes, Carla has earned $\$70$ in commission. For selling 9 suits and 9 pairs of shoes, Benicio has earned $\$126$ in commission. How much is the commission for selling a suit and how much for a pair of shoe's?

\begin{equation}10x+3y=70\textrm{ },\textrm{ }9x+9y=126\end{equation}

9.

Briana's family spend $\$53$ on 3 adult tickets and 8 youth tickets at an amusement park. Max's family spent $\$57$ on 3 adult tickets and 9 youth tickets. What is the price of an adult and a youth ticket?

\begin{equation}3x+8y=53\textrm{ },\textrm{ }3x+9y=57\end{equation}

10.

Carl bought 18 apples of two different varieties to make a pie. The total cost of the apples was $\$126$. Granny Smith apples cost $\$6$ each and Gala apples cost $\$8$ each. How many of each type of apple did Carl buy?

\begin{equation}x+y=18\textrm{ },\textrm{ }6x+8y=126\end{equation}