Video: Solving Word Problems Involving the Same Rate

On a day, a restaurant offered a free drink for 2 out of every 5 customers. If the restaurant received 90 customers that day, how many drinks were given for free?

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Video Transcript

On a day, a restaurant offered a free drink for two out of every five customers. If the restaurant received 90 customers that day, how many drinks were given for free?

We were told in the question that two out of every five customers received a free drink. This can be written as a fraction. As there were 90 customers in total, we need to calculate two-fifths of 90. The word “of” in mathematics means multiply or times. So we need to multiply two-fifths by 90. This could be rewritten as two over five multiplied by 90 over one. Any whole number divided by one is itself. We could work out this calculation by multiplying the two numerators and then multiplying the two denominators separately. However, it is often useful to look to see if we can cross simplify or cross cancel first.

Five and 90 are both divisible by five. Five divided by five is equal to one. And 90 divided by five is equal to 18. We could check the second calculation using the bus stop method. Nine divided by five is one remainder four. So we carry the four. 40 divided by five is equal to eight. Therefore, 90 divided by five equals 18. We can now multiply the two numerators and multiply the two denominators. Two multiplied by 18 is equal to 36. And one multiplied by one is equal to one. 36 divided by one is equal to 36. We can, therefore, conclude that 36 drinks were given for free as two-fifths of 90 equals 36.

We could also have solved this problem by using percentages or decimals. The fraction two-fifths is equivalent to four-tenths as two multiplied by two is equal to four and five multiplied by two is equal to 10. Remember whatever you do to the bottom you must do to the top. Four divided by 10 is equal to 0.4. Therefore, the decimal that is equivalent to two-fifths is 0.4. We could, therefore, have used an alternative method by multiplying 0.4 by 90. 0.4 multiplied by 10 is four. And four multiplied by nine is equal to 36. This method also gives us an answer of 36 free drinks.

0.4 is also equal to 40 percent. This means that our third option would have been to have found 40 percent of 90. To calculate 10 percent of any number, we divide by 10. Therefore, 10 percent of 90 is equal to nine. 10 percent multiplied by four is equal to 40 percent. Therefore, we need to multiply nine by four. This is equal to 36. Therefore, once again we get the answer of 36 free drinks.

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