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3 years ago

the larger of two numbers is two more than five times the smaller number. if the sum of the two numbers is 80, find both numbers

Mathematics

1 answer:

amm18123 years ago

3 0

Answer:

x = 41/3

y = 199/3

Step-by-step explanation:

Solve using system of equations

x is smaller number, y is larger

eq1> y + 2 = 5x > y = 5x - 2

eq2> 80 = x + y > y = 80 - x

equate

80 - x = 5x - 2

Solving:

x = 41/3

y = 199/3

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In the following exercises, solve

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When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.

Step-by-step explanation:

The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of litres with psi, what is the volume if the tank has a psi pressure.

Calculate the volume to the nearest whole number.

Use the given values and calculate the proportionality constant as well as required solution.

Step 1 of 2

Write the inversely proportionality relation between the volume and pressure of a gas in container.

$v \propto \frac{1}{p}$

Where volume is represented by v and pressure is represented by p.

Remove the proportionality and place a constant say k.

$v=\frac{k}{p}$

Substitute the given values of nitrogen that v=29.5 and

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$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$

Step 2 of 2

Substitute the value p=14.7 and above calculated k value in the equation

$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$

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