Hannah and francine have 120. hannah and peter have 230.peter has 6 times as much money sa francine.how much money does hannah have?
h+f = 120
h+p = 230
p = 6f
since p=6f,
h+f = 120
h+6f = 230
subtract top from bottom to get
5f = 110
f = 22
so, h=98
Hannah has 98
Where does the 5f come from??
I understand you subtract, but what determines that you should divide 110 by 5?
To find out how much money Hannah has, we can solve the given equations one by one:
We are given that Hannah and Francine have a total of 120. So, let's represent this as an equation:
Hannah + Francine = 120
We're also given that Hannah and Peter have a total of 230, and Peter has 6 times as much money as Francine. Let's represent this as equations:
Hannah + Peter = 230
Peter = 6 * Francine
Since we need to find out Hannah's money, let's isolate her variable in the equations.
From the equation "Hannah + Francine = 120", we can rewrite it as "Hannah = 120 - Francine".
Substituting the value of Hannah in the equation "Hannah + Peter = 230":
(120 - Francine) + Peter = 230
And substituting Peter's value in terms of Francine:
(120 - Francine) + 6 * Francine = 230
Simplifying the equation:
120 - Francine + 6 * Francine = 230
Combine like terms:
120 + 5 * Francine = 230
Subtracting 120 from both sides:
5 * Francine = 110
Dividing both sides by 5:
Francine = 22
Now, we can substitute the value of Francine back into the equation "Hannah = 120 - Francine" to find out Hannah's money:
Hannah = 120 - 22
Hannah = 98
Therefore, Hannah has 98 units of money.