Video: Solving Word Problems Involving Ratios

A piece of land with an area of 80 acres will be shared between a school, a park, and a hospital. The school will get 8 acres and the remainder will be shared between the park and the hospital in the ratio 2 : 1. What area of land will each of the park and the hospital get?

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Video Transcript

A piece of land with an area of 80 acres will be shared between a school, a park, and a hospital. The school will get eight acres. And the remainder will be shared between the park and the hospital in the ratio two to one. What area of land will each of the park and hospital get?

We’re told in the question that there was a total of 80 acres. Of these 80 acres, the school receives eight acres. Subtracting eight from 80, we’ll calculate the total land between the park and the hospital. 80 minus eight is equal to 72. This means that the park and hospital will share 72 acres between them.

We’re told that they share this land in the ratio two to one. As the park gets two parts and the hospital gets one part, there are three parts in total. We need to divide the 72 acres by three. One way of doing this is using the bus stop method. Seven divided by three is equal to two remainder one. And 12 divided by three is equal to four.

This means that 72 divided by three is equal to 24. We can therefore say that one part of the ratio is equal to 24 acres. As the park received two parts, we need to multiply 24 by two. This is equal to 48, as two multiplied by 20 is 40 and two multiplied by four is eight. The hospital received one part. And one multiplied by 24 is 24.

We can therefore conclude that the park received 48 acres and the hospital received 24 acres. A quick check at this point would be to add 48, 24, and eight and make sure that our total was equal to 80. As these three numbers do sum to 80, we know that our answer is sensible. The park has 48 acres and the hospital 24 acres.

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