750 inches

Asked by maham237 @ 03/01/2021 in Mathematics viewed by 148 People

A worker uses 750 inches of steel wire to make 300 springs of the same size. At this rate how many inches of steel wire are needed to make 1 spring?

Answered by maham237 @ 03/01/2021

Answer:

2.5 inches of steel wire are needed to make one spring.

Step-by-step explanation:

In order to answer this, we can set up a proportion (setting two fractions equal to each other) to solve for how many inches of steel wire are needed to make one spring.

We are given a ratio: 750 inches of steel wire are required to make 300 springs. Therefore, this is represented as:

$\bullet \ \ \ \text{750 inches of steel wire : 300 springs}$

This can be rewritten in fraction form:

$\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}}$

Therefore, we have our first proportion.

We want to make one spring, so we need to find how much steel is required to make one spring. Therefore, for our second fraction, the inches of steel wire is unknown. We can define this as x.

$\bullet \ \ \ \text{x inches of steel wire}$

Finally, our ratio can be written in the same manner as the previous ratio:

$\bullet \ \ \ \text{x inches of steel wire : 1 spring}$

This can be rewritten in fraction form:

$\displaystyle \bullet \ \ \ \frac{\text{x inches of steel wire}}{\text{1 spring}}$

Now, we need to set up our proportion. We do this by setting our two ratios equal to each other.

$\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{x inches of steel wire}}{\text{1 spring}}$

To solve a proportion, we need to cross multiply. We can flip our fractions and solve for the reciprocal since there is not really a way to represent cross-multiplication.

$\displaystyle \bullet \ \ \ \frac{\text{750 inches of steel wire}}{\text{300 springs}} = \frac{\text{1 spring}}{\text{x inches of steel}}$

First, we can drop our labels/units.

$\displaystyle \bullet \ \ \ \frac{750}{300} = \frac{1}{\text{x}}$

Then, we can multiply across.

$\displaystyle \bullet \ \ \ 750 = 300x$

Finally, we can solve for x.

$\displaystyle 750 = 300x\\\\\frac{750}{300}=\frac{300x}{300}\\\\2.5 = x\\\\x = 2.5$

Therefore, to make one spring, exactly 2.5 inches of steel wire are needed.

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