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Algebra

Resources for Basic and Advanced Algebra

Find three consecutive integers such that

Find three consecutive integers such that four times the smallest of the integers is three times the largest. What is the largest of these three integers?

Solution:

To solve for the 3 consecutive integers, we need to have these representations: Read more »

The annual sophomore class picnic is a plan by committee consisting of 17 members.

The annual sophomore class picnic is a plan by committee consisting of 17 members. A vote to determine whether the picnic should be held at the beach or in the mountains resulted in a victory for the beach location. However if the two committee members had changed the vote from favoring the beach to favoring the mountains, the mountain site would have won by one vote. How many votes did each picnic location receive?

Solution:

Based on the problem data, let us use the following variable representation:

            x = beach voter
           y = mountain voter
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The profits of a business are shared among three stockholders

The profits of a business are shared among three stockholders. The first stockholder receives twice as much as the second and the second receives three times as much as the third. If the profits for last year were $ 26,400, how much did each stockholder receive? Read more »

A parking meter slot receives dimes and nickels

A parking meter slot receives dimes and nickels. When the meter box was emptied there were 148 coins and a total of $ 10.65. How many dimes and how many nickels were there? Read more »

Admission tickets to a local circus show were priced at USD4 for adult and USD3 for the student.

Admission tickets to a local circus show were priced at 4 dollars for adult and 3 dollars for the student. For the first 3 days of the show, 810 tickets were sold and the total receipts were $2853. How many of the each type of ticket were sold? Read more »

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