Tyrone has $60 and his sister has $135. Both get an allowance of $5 each week. Tyrone decides to save his entire allowance, but his sister spends all of hers each week plus an additional $10 each week. After how many weeks will they each have the same amount of money?
Tyrone starts with 60.
Sister starts with 135.
Each receives $5/week. Let w = weeks.
Tyrone will have
60 + $5*w after w weeks.
Sister will have 135 + $5*w - $5*w - $10*w.
Set them equal and solve for w. Post your work if you get stuck.
Well, if Sister spends all of her allowance each week and an additional $10, it sounds like she might need some financial advice. Maybe she should consider investing in a piggy bank. Or in stocks...I hear the bacon industry is booming.
But let's get back to the question at hand. We want to find out after how many weeks Tyrone and his sister will have the same amount of money.
We can set up an equation to represent this situation:
60 + 5w = 135 + 5w - 5w - 10w
Now let's simplify this equation. We see that the 5w terms cancel out, leaving us with:
60 = 135 - 10w
To isolate w, we can subtract 135 from both sides:
-75 = -10w
Now, we can divide both sides by -10 to solve for w:
w = (-75)/(-10)
Luckily, dividing negative numbers is a positive thing! So, w = 7.5.
But wait, we can't have half a week! That would be ridiculous. So, let's round up and say that after 8 weeks, Tyrone and his sister will have the same amount of money.
And maybe by then, Sister will have learned a thing or two about saving money. But I wouldn't count on it.
Let's set up the equation to find the number of weeks it takes for Tyrone and his sister to have the same amount of money.
Tyrone's total money after w weeks: 60 + 5w
Sister's total money after w weeks: 135 + 5w - 5w - 10w
We can simplify Sister's equation: 135 - 10w
Now let's set the two equations equal to each other:
60 + 5w = 135 - 10w
Combine like terms:
15w = 75
Divide both sides by 15:
w = 5
So it will take 5 weeks for Tyrone and his sister to have the same amount of money.
Explanation of how to solve the equation:
1. Start by setting up the equation for Tyrone and Sister's total money after w weeks.
2. Simplify Sister's equation by combining like terms.
3. Set the two equations equal to each other.
4. Combine like terms on both sides of the equation.
5. Isolate the variable w by performing the necessary operations (in this case, dividing both sides by 15).
6. Solve for w to find the number of weeks it takes for Tyrone and his sister to have the same amount of money.
It is 5 weeks.
5x+60=y
5x+135-15x=y
set equations equal to each other to see when they will have the same amount in each situation
5x-5x+15x=135-60
15x=75
x=75/15=5