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?
Francine has $X.
Peter has $6X.
Hannah hss $Y.
Eq1: X + Y = 120.
Eq2: 6X + Y = 230.
Multiply Eq1 by -1 and add the Eqs:
-X + -Y = -120
6X + Y = 230
Sum: 5x = 110,
X = $22.
X + Y = 120,
Y = 120 - X = 120 - 22 = $98.
To solve this problem, we can use a system of equations. Let's assign variables to 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 clue, we know that Hannah and Francine have $120, so we can write the equation:
H + F = 120 ............(Equation 1)
From the second clue, we know that Hannah and Peter have $230, so we can write the equation:
H + P = 230 ............(Equation 2)
The third clue states that Peter has 6 times as much money as Francine, so we can write the equation:
P = 6F .................(Equation 3)
Now we have a system of three equations: Equation 1, Equation 2, and Equation 3. We can solve this system to find the values of H, F, and P.
Let's solve the system by substituting the value of P from Equation 3 into Equation 2:
H + 6F = 230
Now, we can use this new equation and Equation 1 to eliminate H and solve for F.
(H + 6F) - (H + F) = 230 - 120
Simplifying, we get:
5F = 110
Dividing both sides by 5, we get:
F = 22
Now that we have the value of F, we can substitute it back into Equation 3 to find the value of P:
P = 6F
P = 6(22)
P = 132
Finally, to find the value of H, we can substitute the values of F and P into Equation 2:
H + P = 230
H + 132 = 230
H = 230 - 132
H = 98
Therefore, Hannah has $98.