at a restaurant brandy paid twice as much as Katie and Katie paid $3 more than Stephanie if the total combined amount they paid was $56 how much did Katie pay
Katie's share ---- x
Brandy --------- 2x
Steph-----------x-3
x + 2x + x-3 = 56
4x = 59
x = 14.75
Katie --- $14.75
Brandy --$29.50
Steph---$ 11.75
check:
14.75+29.50+11.75 = 56
All is good.
To find out how much Katie paid, we can follow these steps:
Step 1: Let's assign variables to the unknown amounts we need to find.
- Let's assume Stephanie paid x dollars.
- Katie paid $3 more than Stephanie, so Katie paid (x + $3).
- Brandy paid twice as much as Katie, so Brandy paid 2 * (x + $3).
Step 2: We know that the total combined amount they paid was $56. So, we can write the equation:
x + (x + $3) + 2 * (x + $3) = $56
Step 3: Simplify the equation:
x + x + $3 + 2x + $6 = $56
4x + $9 = $56
Step 4: Subtract $9 from both sides of the equation:
4x = $56 - $9
4x = $47
Step 5: Divide both sides of the equation by 4 to isolate x:
x = $47 / 4
x = $11.75
So, Stephanie paid $11.75.
Step 6: Now, let's find out how much Katie paid by substituting the value we found for x back into the equation:
Katie paid (x + $3) = $11.75 + $3 = $14.75
Therefore, Katie paid $14.75 at the restaurant.