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A florist was packing some roses and lilies into 2 boxes. She packed 1/3 of the flowers into Box A and the rest into Box B. The ratio of the number of roses to lilies in Box A was 1 : 3 and it was 3:1 in Box B. What was the ratio of the total number of roses to the total number of lilies?​

Respuesta :

Answer is the ratio 7:5

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Explanation:

r = number of roses in box A, some positive whole number

roses : lilies = 1:3

roses : lilies = 1r:3r

Box A has 1r+3r = 4r flowers.

Let T be the number of flowers total. We're told that 1/3 of the total goes to box A.

1/3 of T = 4r for box A

T/3 = 4r

T = 3*4r

T = 12r

There are 12r flowers total when combining both boxes.

Since 1/3 of the total goes to box A, this means 2/3 goes to box B.

2/3 of T = (2/3)*(12r) = 8r flowers go to box B

In short,

  • 4r = number of flowers in box A
  • 8r = number of flowers in box B

The two counts add to 12r again. Also note that 8r is twice that of 4r.

The roses to lilies ratio in box B is 3:1, which means the roses count is 3 times that of the lilies. We'll split the 8r into 4 equal pieces since 3+1 = 4.

8r/4 = 2r

This represents the number of lilies in box B.

The number of roses is three times as much, so 3*(2r) = 6r is the number of roses.

As a check, (number of roses in box B) + (number of lilies in box B) = (6r) + (2r) = 8r flowers total for box B.

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Let's recap so far

  • r = number of roses in box A
  • 3r = number of lilies in box A
  • 6r = number of roses in box B
  • 2r = number of lilies in box B

We have r+6r = 7r roses total and 3r+2r = 5r lilies total.

The ratio of total roses to total lilies is 7r:5r. Divide both parts by the GCF r and we end up with the final answer of 7:5

francocanacari

The ratio of the total number of roses to the total number of lilies is 3:1.

Ratios

Given that a florist was packing some roses and lilies into 2 boxes, and she packed 1/3 of the flowers into Box A and the rest into Box B, and the ratio of the number of roses to lilies in Box A was 1 : 3 and it was 3:1 in Box B, to determine what was the ratio of the total number of roses to the total number of lilies, the following calculation must be made:

  • 1:3 + 3:1 = 4:4
  • 4:4 x 1/3 = 1/3

Therefore, the ratio of the total number of roses to the total number of lilies is 3:1.

Learn more about ratios in https://brainly.com/question/13157407

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