You and your brother are saving money to buy a camcorder. You already have
$60 saved and your brother has $45 saved. You plan on saving an additional
$5 each week. Your brother plans on saving an additional $8 each week.
Write and solve an equation to find how many weeks it takes both of you to
save the same amount. Let w represent the number of weeks.

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mastercookie55 mastercookie55 · Answer 1 · 2020-09-23T06:07:36+02:00

Answer:

5 weeks.

Step-by-step explanation:

We have $60, and we're saving an additional $5 each week:

[tex]60+5w[/tex]

Our brother has $45, and is saving an additional $8 each week:

[tex]45+8w[/tex]

Let's set up an equation:

[tex]60+5w=45+8w[/tex]

We had to set these two expressions equal to each other because our end result should be equal.

Subtract [tex]60[/tex] from both sides of the equation:

[tex]5w=-15+8w[/tex]

Subtract [tex]8w[/tex] from both sides of the equation:

[tex]-3w=-15[/tex]

Divide by the coefficient of [tex]w[/tex], which is [tex]-3[/tex]:

[tex]w=5[/tex]

Check your work:

You can check your work with substitution. Take the initial equation and substitute [tex]w[/tex] with [tex]5[/tex]:

[tex]60+5(5)=45+8(5)[/tex]

Simplify:

[tex]85=85[/tex]

It checks out!