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A florist sells roses, violets, and tulips. If 7/20 of the flowers in her store are roses, and 8/15 of the flowers are violets, what part of the total number of flowers in her store are tulips?

A. 1/12
B. 1/10
C. 1/8
D. 1/5

User AmmoPT
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2 Answers

2 votes

Final answer:

To determine the part of the total number of flowers that are tulips, we find the sum of the fractions of roses and violets and subtract from 1. The flowers are 7/20 roses and 8/15 violets, leaving 7/60 as tulips after calculations.

Step-by-step explanation:

Let's determine what part of the total number of flowers in the florist's store are tulips. Since 7/20 of the flowers are roses and 8/15 of the flowers are violets, we first need to calculate the fraction of the store's flowers that these two types make up together.

The Least Common Denominator (LCD) for 20 and 15 is 60. To find out the equivalent fractions with a denominator of 60, we multiply the numerator and denominator of 7/20 by 3 to get 21/60, and we multiply the numerator and denominator of 8/15 by 4 to get 32/60. Adding these two fractions, we get 21/60 + 32/60, which equals 53/60.

Since all flowers in the store are either roses, violets, or tulips, the remaining flowers must be tulips. Subtracting the fraction of roses and violets from the total, we get 1 - 53/60 = 7/60. This fraction cannot be simplified any further, so 7/60 is the fraction of the total flowers that are tulips. However, this answer is not listed in the provided options, suggesting there might be a mistake in the question or the options given.

1

User MetaSnarf
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7.8k points
6 votes

Final Answer:

The part of the total number of flowers that are tulips is 1/8. (Option C is the correct answer.)

Step-by-step explanation:

Proportion of Roses and Violets: We know that 7/20 of the flowers are roses and 8/15 are violets. These two proportions represent parts of the whole, so their sum should not exceed 1 (representing all flowers).

Calculating Remaining Proportion: To find the proportion of tulips, we need to subtract the combined proportion of roses and violets from 1 (the total):

Tulips proportion = 1 - Roses proportion - Violets proportion

Tulips proportion = 1 - 7/20 - 8/15

Tulips proportion = (60 - 28 - 32) / 60

Tulips proportion = 20 / 60

Tulips proportion = 1/3

Simplifying the Fraction: We can further simplify the fraction 1/3 to 1/8 by multiplying the numerator and denominator by 8:

Tulips proportion = 1/3 * 8/8

Tulips proportion = 8/24

Tulips proportion = 1/8

Therefore, 1/8 of the flowers in the store are tulips.

Option C is answer.

User Pouya Zad
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8.1k points