jen and heather went to lunch. when the bill came, jen discovered she had only$6. luckily, heather had enough money to pay the other part, or three fifths. how much did heather pay? how much was the bill?
(2/5)x = 6
x = 6 / (2/5)
x = 6 * (5/2)
x = 30/2 = 15
6 = (2/5) (total)
To find out how much Heather paid and the total bill amount, we can break down the information given in the question.
Let's consider:
Amount Jen had = $6
Remaining amount paid by Heather = three fifths
To determine the amount Heather paid, we need to calculate three fifths of the total bill. However, we don't have the total bill amount yet.
Since Jen had $6 and Heather paid the remaining amount, we can set up the equation:
Jen's contribution + Heather's contribution = Total bill amount
Since Heather paid three fifths of the bill, we can write it as a fraction: 3/5.
Now, let's assign some variables:
Total bill amount = x (unknown)
Jen's contribution = $6
Heather's contribution = (3/5) * x (since it's three fifths of the total bill)
We can now set up the equation:
$6 + (3/5) * x = x
To solve this equation, we can first get rid of the fraction by multiplying throughout by 5:
5 * $6 + 3 * x = 5 * x
30 + 3x = 5x
Next, we can simplify the equation by bringing all the x terms to one side:
5x - 3x = 30
2x = 30
To solve for x, we divide both sides of the equation by 2:
(x = 30) / 2
x = 15
Therefore, the total bill amount (x) is $15.
Now we can calculate Heather's contribution, which is three fifths of the total bill:
Heather's contribution = (3/5) * $15
Heather's contribution = $9
So, Heather paid $9, and the total bill amount was $15.