Monica and Max Gordon each want to buy a scooter. Monica has already saved $25 and plans to save $5 per week until she can buy the scooter. Max has $16 and plans to save $8 per week. How many weeks will it take Monica and Max to have saved the same amount of money? How much money would they have at that time?
Monica : y=5x+25
Max :y=8x+16
the weeks Monica and Max have saved the same amount of money :
5x+25=8x+16
x=3 weeks
the money they would have at that time : Y=5x+16 when x=3 :y =$40
To find out how many weeks it will take Monica and Max to have saved the same amount of money, we can set up and solve an equation.
Let's represent the number of weeks as "w".
For Monica:
Money saved by Monica = $25 + $5 * w
For Max:
Money saved by Max = $16 + $8 * w
We want to find the value of "w" when the money saved by Monica is equal to the money saved by Max.
So, we can set up the equation:
$25 + $5 * w = $16 + $8 * w
Now, let's solve this equation to find the value of "w".
$5 * w - $8 * w = $16 - $25
-$3 * w = -$9
Dividing both sides by -3:
w = -$9 / -$3
w = 3
Therefore, it will take them 3 weeks to have saved the same amount of money.
To find out how much money they will have at that time, we can substitute the value of "w" into either Monica's or Max's equation.
Let's use Monica's equation:
Money saved = $25 + $5 * 3
Money saved = $25 + $15
Money saved = $40
So, after 3 weeks, both Monica and Max will have saved $40.