2. 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?
80 + 10x = 275 -15x
25x = 355
x = number of weeks.
Go back to the original 80 + 10x to find c.
A. To model this situation mathematically, we can represent the amount of money you have as $80 + $10n, where n represents the number of weeks. Similarly, we can represent the amount of money your brother has as $275 - ($15 * n), where n also represents the number of weeks.
B. To find out how long it will take for you to have as much money as your brother, we need to set the two expressions equal to each other and solve for n:
$80 + $10n = $275 - ($15 * n)
Simplifying the equation:
$10n + ($15 * n) = $275 - $80
$25n = $195
Dividing both sides of the equation by 25:
n = $195 / $25
n = 7.8
Therefore, it will take approximately 7.8 weeks for you to have as much money as your brother. Since we can't have a fraction of a week, we need to round up to the nearest whole number of weeks.
C. To determine how much you have saved when you catch up to your brother, we substitute the value of n into the expression representing the amount of money you have:
$80 + $10n = $80 + $10 * 7.8 ≈ $80 + $78 = $158
So, you will have saved approximately $158 when you catch up to your brother.