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One pipe can fill in tank in 45 minutes and another pipe can fill it in 30 minutes.

One pipe can fill in tank in 45 minutes and another pipe can fill it in 30 minutes. If these two pipes are open and a third pipe is draining water from the tank, it takes 27 min to fill the tank. How long will it take the third pipe alone to empty a full tank?

 

When the smaller of two consecutive integers is added to three times the larger

When the smaller of two consecutive integers is added to three times the larger, the result is 51. Find the integers.

Solution:

To find the two consecutive integers, we need the following representations. Read more »

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 »

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