# Question Video: Solving Word Problem Involving Percentages Mathematics • 7th Grade

A vase contains some flowers. 20% of the flowers are pink, 48% of the flowers are violet, and the rest are red. Given that the vase contains 10 pink flowers, calculate how many violet flowers and how many red flowers it contains.

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### Video Transcript

A vase contains some flowers. 20 percent of the flowers are pink, 48 percent of the flowers are violet, and the rest are red. Given that the vase contains 10 pink flowers, calculate how many violet flowers and how many red flowers it contains.

So we know that 20 percent of the total number of flowers are pink. 48 percent are violet. And the rest are red. All together, the flowers should represent 100 percent. So if we take away the percentage of pink flowers and the percentage of violet flowers, we will find the percentage of red flowers. 100 minus 20 minus 48 will be 32.

So, 32 percent of the total number of flowers will be red. And we’re actually given that the vase contains 10 pink flowers. So we can plug that in here.

In mathematics, the word “of” means to multiply. So we can replace the word “of” with multiplication. So if we could find the total number of flowers, we could find the number of violet flowers and the number of red flowers.

Taking this first equation, we can solve for the total. We would need to divide both sides of the equation by 20 percent. 20 percent can be rewritten by dropping the percent sign and moving the decimal place two places to the left. Or think of moving the numbers two places to the right.

So taking 20 and dividing by 100, that’s what would give us the .20. And 10 divided by .20 is 50. So there are total of 50 flowers. So we can replace the word “total” with 50 and then solve for violet and red.

48 percent would be 0.48 dropping the percentage sign and dividing by 100. So .48 times 50 would give us 24. So there will be 24 violet flowers. 32 percent can be written as 0.32. And then multiplying by 50 gives us 16. There are 16 red flowers.

So all of these flowers together, the 10 pink, 24 violet, and 16 red, should add together to be 50. In the ones place, four plus six is 10. So we write zero, carry the one, and then one plus one plus two plus one is five. So there’ll be 50 total.

So the number of violet flowers will be 24 and the number of red flowers will be 16.