You have $80 and your brother has $275 dollars. You save $10 of your allowance each week. Your brother spends his allowance plus $15 each week.
A. Write an equation to model this.
B. How long before you have as much money as your brother?
C. How much have you saved when you catch up to him?
your equation:
y = 80 + 10n
your brother's equation:
y = 275 - 15n
b) when does
80+10n = 275-15n ?
c) whatever you got for n in b) sub this into "your" equation
A. To model this situation, we can create an equation based on the information given. Let's use the variables "x" to represent the number of weeks.
For your savings, the equation is: your total savings = $80 + $10 per week
For your brother's savings, the equation is: your brother's total savings = $275 - $15 per week
B. To find out how long before you have as much money as your brother, we need to set up an equation where your total savings will be equal to your brother's total savings.
So, we can set up the equation:
$80 + $10x = $275 - $15x
Simplifying the equation:
$10x + $15x = $275 - $80
$25x = $195
Dividing both sides of the equation by 25:
x = 7.8
Since it doesn't make sense to have a fraction of a week, we can round up the result to the nearest whole number.
So, it will take approximately 8 weeks before you have as much money as your brother.
C. To find out how much you have saved when you catch up to your brother, we can substitute the value of "x" (which is 8) into the equation for your savings:
Your total savings = $80 + $10x
Your total savings = $80 + $10(8)
Your total savings = $80 + $80
Your total savings = $160
So, when you catch up to your brother after 8 weeks, you will have saved $160.