Hannah and Francine have $120. Hannah and peter have $230. Peter has 6 times as much money as Francine. How much does Hannah have?
p = 6f
now write the other facts as algebra, and then solve the equations.
To find out how much Hannah has, let's break down the information given:
1. Hannah and Francine have a total of $120.
2. Hannah and Peter have a total of $230.
3. Peter has 6 times as much money as Francine.
Let's use algebraic representation for the unknowns:
- Let "H" represent the amount of money Hannah has.
- Let "F" represent the amount of money Francine has.
- Let "P" represent the amount of money Peter has.
From the first statement, we know that H + F = $120.
From the second statement, we know that H + P = $230.
Since Peter has 6 times as much money as Francine, we can write the equation P = 6F.
Now, let's solve the system of equations:
First, substitute P = 6F in the second equation: H + 6F = $230.
Next, combine like terms: H + 6F = $230.
Subtract H from both sides: 6F = $230 - H.
Now, let's substitute H = $120 - F into the equation above: 6F = $230 - ($120 - F).
Simplify: 6F = $230 - $120 + F.
Combine like terms: 6F - F = $110.
Simplify: 5F = $110.
Divide both sides by 5: F = $110 / 5.
Therefore, Francine has F = $22.
Now, we can substitute F = $22 into the equation P = 6F: P = 6 * $22.
Calculate: P = $132.
Finally, we can substitute F = $22 and P = $132 into the equation H + P = $230 to find the value of H: H + $132 = $230.
Subtract $132 from both sides: H = $230 - $132.
Calculate: H = $98.
Therefore, Hannah has $98.