Question

show work please~

there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

for every 1 cup of blue paint, ___ cups of red paint are needed

for every 1 cup of red paint, ___ cup of blue paint is needed

for every 4 cups of red paint,___ cups of blue paint are needed

Answer 1

For every 1 cup of blue paint, $\frac{10}{4}$ cups of red paint are needed

For every 1 cup of red paint, $\frac{4}{10}$ cup of blue paint is needed

For every 4 cups of red paint, $\frac{16}{10}$ cups of blue paint are needed

Solution:

Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

Therefore, ratio is

$Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}$

For every 1 cup of blue paint, ___ cups of red paint are needed

Let "x" be the cups of red paint needed

Then we get,

$\frac{10}{3} : \frac{4}{3}\\\\x : 1$

This forms a proportion

$1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}$

Therefore, 10/4 cups of red are needed for 1 cup of blue

For every 1 cup of red paint, ___ cup of blue paint is needed

Let "x" be the cups of blue paint needed

Then, we get

$\frac{10}{3} : \frac{4}{3}\\\\1 : x$

This forms a proportion

$\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}$

Thus, 4/10 cups of blue are needed for 1 cup of red paint

For every 4 cups of red paint,___ cups of blue paint are needed

Let "x" be the cups of blue paint needed

Then, we get

$\frac{10}{3} : \frac{4}{3}\\\\4 : x$

This forms a proportion

$\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}$

Thus 16/10 cups of blue paint are needed for every 4 cups of red paint