Question

A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed.

The city will have (blank) streetlights at the end of 46 weeks.
The city will have 232 streetlights at the end of (blank) weeks.

Answer 1

316 street lights.

25 weeks.

Explanation:

Linear Equations:

We can set up a linear equation with the information provided expressed in slope intercept form:
`y=mx+b`, where "m" is the slope, and "b" is the initial value.

We're given the initial amount, or what the city already has is 132 street lights, that's our "b" value and they will install 4 each additional week which is our slope. So we have the equation:
`y=4x+132`

To find how many streetlights the city will have at the end of 46 weeks, we can plug in 46 as "x" to give us:

`y=4(46)+132\\y=316`

To find when the city will have 232 streetlights we can set the equation equal to 232 and solve for "x" the number of weeks.

`232=4x+132`

Subtract 132 from both sides

`100=4x`

Divide both sides by 4

`25=x`

So this will occur after 25 weeks.