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neonofarm [45]
3 years ago
9

Show work please~

Mathematics
1 answer:
love history [14]3 years ago
5 0

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

<em><u>Solution:</u></em>

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}

<h3><u>For every 1 cup of blue paint, ___ cups of red paint are needed</u></h3>

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

<h3><u>For every 1 cup of red paint, ___ cup of blue paint is needed</u></h3>

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

<h3><u>For every 4 cups of red paint,___ cups of blue paint are needed</u></h3>

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

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From 1980 to 1990, Lior’s weight increased by 25%

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Let "x" be the weight in kilograms in 1980

<em><u>The percentage increase is given by formula:</u></em>

\text{Percentage increase } = \frac{\text{Final value - initial value}}{\text{initial value}} \times 100

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Initial value in 1980 = x

Final value in 1990 = k

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25 = \frac{k-x}{x} \times 100\\\\25x = 100(k-x)\\\\x = 4(k-x)\\\\x = 4k - 4x\\\\5x = 4k\\\\x = \frac{4k}{5}

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