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?

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:

This can be rewritten in fraction form:

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.

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

This can be rewritten in fraction form:

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

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.

First, we can drop our labels/units.

Then, we can multiply across.

Finally, we can solve for x.

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

2.5 inches steel wire

We can use an equation to find the answer. 750/300 = 2.5

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,