Question

A gardener planted flowers of different colors.
of the flowers are yellow
The gardener planted 119 purple flowers. How many flowers did the
gardener plant?
of the remaining flowers are green.
• The rest of the flowers are purple. HELP FAST IM AWARDING BRAINLYEST

Answer 1

Question:

A gardener planted flowers of different colors.

3/10 of the flowers are yellow.

3/4 of the remaining flowers are green.

The rest of the flowers are purple.

The gardener planted 119 purple flowers, how many flowers did the gardener plant?

Answer:

$Total = 680$

Step-by-step explanation:

Represent Yellow with Y, Green with G and Purple with P

$Y = \frac{3}{10}$

First, we need to determine the fraction of the rest.

$Yellow + The\ Rest = 1$ ---- In terms of fraction

$The\ Rest = 1 - Yellow$

$The\ Rest = 1 - \frac{3}{10}$

$The\ Rest = \frac{10 - 3}{10}$

$The\ Rest = \frac{7}{10}$

We have that:

$G = \frac{3}{4} * The\ Rest$

$G = \frac{3}{4} * \frac{7}{10}$

$G = \frac{21}{40}$

To solve for the fraction of Purple, we make use of:

$Y + G + P = 1$

$P = 1 - Y - G$

Recall that: $Y = \frac{3}{10}$ and $G = \frac{21}{40}$

So:

$P = 1 - \frac{3}{10} - \frac{21}{40}$

$P = \frac{40 - 12 - 21}{40}$

$P = \frac{7}{40}$

At this point, we have the fraction of each flower as:

$Y = \frac{3}{10}$

$G = \frac{21}{40}$

$P = \frac{7}{40}$

Also, we have that:

$P = 119$

The relationship between both values of P is:

$\frac{7}{40} * Total = 119$

$Total = 119 * \frac{40}{7}$

$Total = \frac{119 * 40}{7}$

$Total = \frac{4760}{7}$

$Total = 680$