Hannah and Francine have $120. Hannah and Peter have $230. Peter has 6 times as much money as francine. How much money does Hannah have?
To find out how much money Hannah has, we can use algebraic equations to solve the problem.
Let's assign variables to the unknown quantities:
- Let's say Hannah has x dollars.
- Since Peter has 6 times as much money as Francine, let's say Francine has y dollars. Therefore, Peter has 6y dollars.
According to the problem:
1. Hannah and Francine have $120, so their total is x + y = $120. (Equation 1)
2. Hannah and Peter have $230, so their total is x + 6y = $230. (Equation 2)
To solve this system of equations, we can use a method called substitution:
1. Rearrange Equation 1 to solve for x: x = $120 - y.
2. Substitute x in Equation 2 with $120 - y: $120 - y + 6y = $230.
3. Simplify the equation: 120 + 5y = 230.
4. Subtract 120 from both sides: 5y = 110.
5. Divide both sides by 5: y = 22.
Now that we know Francine has $22, we can substitute this value into Equation 1 to find Hannah's money:
x + y = $120
x + 22 = $120
Subtract 22 from both sides: x = $98.
Therefore, Hannah has $98.