Question

A builder wants to build a bridge whose cross section is 55ft 6in wide an equation to find the distance b in feet between each beam Is...

Answer 1

An equation is used to represent expressions with equal values. The equation to find the value of b is: $55.5ft = 5b + 10.5ft$

Given that:

$Width = 55ft\ 6in$

To get the value of distance b, we simply add up the length of every item that makes up the cross-section.

So, we have:

$Width = 3ft + \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b+ \frac 34 ft +b + \frac 34 ft +3ft$

Collect like terms

$Width = b + b + b + b + b + 3ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft + \frac 34 ft +3ft$

$Width = 5b + 10\frac 12 ft$

Substitute $Width = 55ft\ 6in$

$55ft\ 6in = 5b + 10\frac 12 ft$

$5ft\ 6in = 5b + 10.5ft$

Convert inches to feet

$55ft + \frac{6}{12}ft = 5b + 10.5ft$

$55ft + 0.5ft = 5b + 10.5ft$

$55.5ft = 5b + 10.5ft$

Collect like terms

$5b = 55.5ft -10.5ft$

$5b = 45ft$

Divide both sides by 5

$b = 9ft$

Hence:

• An equation to find the value of b is: $55.5ft = 5b + 10.5ft$.
• And the value of b is 9 ft

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