The number of lava cakes on display at a cafe was 3/4 of the number of cupcakes on display. After 20 lava cakes were bought and the staff added another 30 cupcakes, the number of cupcakes was twice the number of lava cakes. The last group of customers bought 5 cupcakes each, finishing all the cupcakes on display. How many customers were there in the last group?
if the cupcake is 20, lava cake is 3/4x
2(3/4x - 20) = 70 + 30
3/2x - 40 = x + 30
1/2x = 70
x = 140
140 + 30 = 170
170 รท 5
= 34
To find the number of customers in the last group, we need to work through a series of steps and calculations based on the given information. Let's break it down:
Step 1: Establish Variables
Let's assign variables to make the problem easier to understand and solve.
Let "l" represent the initial number of lava cakes.
Let "c" represent the initial number of cupcakes.
Step 2: Formulate Equations
Based on the given information, we can set up two equations:
1) The number of lava cakes on display was 3/4 of the number of cupcakes:
l = (3/4)c
2) After 20 lava cakes were bought and 30 cupcakes were added, the number of cupcakes was twice the number of lava cakes:
c + 30 = 2(l - 20)
Step 3: Solve the Equations
Let's solve the equations to find the values of "l" and "c."
From equation 1, we can rewrite "l" in terms of "c":
l = (3/4)c
Plugging this value of "l" into equation 2:
c + 30 = 2((3/4)c - 20)
Let's simplify the equation:
c + 30 = (3/2)c - 40
Combine like terms:
c - (3/2)c = -30 - 40
(1/2)c = -70
Multiply both sides of the equation by 2:
c = -140
This means that the initial number of cupcakes was negative, which is not possible. Therefore, there is an error in the given information or the formulation of the problem.
Double-check the information and equations provided to ensure accuracy.