A certain bakery sells six different-sized wedding cakes

Being simple is the key my friend .
You should not try to be fancy when a simple approach is right in front of your eyes.

This is essentially an algebra problem with two unknown variables.

Let the price of FIRST (ALSO THE SMALLEST) CAKE be Y
Then every other cake will become {Y+X}, {Y+X+X} ......and so on

BASED ON THE INFO, YOU WILL GET:-

First cake price = y
Second cake price = y+x
Third cake price= y+x+x
Fourth cake price = y+x+x+x
Fifth cake price= y+x+x+x+x
sixth cake price = y+x+x+x+x+x

SIXTH CAKE IS LARGEST
y+5x= 24.50

Total price of all cakes =(FIRST $ + SECOND $ + THIRD $....... + SIXTH $) ====> 6y+15x = 109.40

Now you got two unique equation for two unknown variable

WHATS THE PRPBLEM THEN :- SOLVE IT
y+5x=24.50 (Multiply by 3) ...........Eq1
6y+15x=109.40 ............. Eq2
Subtract Eq1 from Eq2

y==>12

put value of y in Eq 1
12+5x=24.50
5x= 12.50
x=\(\frac{12.50}{5}\) ===>2.5 (OPTION D)
ANSWER IS D

ENJOY

109.5= 24.5x6 - 15X
X=2.5


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How did you came up with 15X?

Let L6 represents the price of largest and L1 represents the smallest.

We are given that L6 = 24.5

L5 = 24.5-x ( each smaller sized is x less than its immediate larger)

L4 = 24.5 - 2x

L3 = 24.5 - 3x

L2 = 24.5 - 4x

L1 = 24.5 - 5x

Now, the sum of all prices = 109.5

So, L6 to L1, you will get

109.5= 24.5x6 - 15x

or x = 2.5

From the question we can derive the following equation:

(24.50-5x) + (24.50-4x)+... = 109.50

simplifies to... 24.50(6)-15x=109.50

Solve for x.

x=2.5

I first saw what 25*6 is just to give a ball park number and it was 150. I then realized that the numbers had to decrease by the "biggest" answer values.

I first started with D just b/c it ended in a .50. Once you start to go down the numbers you'll see that in order to end with a .50 (109.5) you need to have an amount taken away that ends in .50. B,C, and E are out. D worked.

Since the price of each cake is reducing by a constant value all the time, the prices will from Arithmetic Series
Average of 6 terms in Arithmetic is average of 3rd and 4th term. Thus now using options
Option C
4th term is 24.5 - 2*2 = 20.5
3rd term is 20.5-2 = 18.5
Average is 19.5
Total price of all 6 is 19.5*6 = 19*6+0.5*6 = 117
But since we need answer less than 117 (109.5) average value is less than 19.5.
Thus moving down to option D
4th term = 24.5-2*2.5 = 19.5
3rd term = 19.5 - 2.5 = 17
Average = 18.25
Total price = 18.25*6 = 18*6+0.25*6 = 108+1.5 = 109.5
Matching with question
Thus answer is option D

We can create the following equation:

(24.50) + (24.50 - x) + (24.50 - 2x) + (24.50 - 3x) + (24.50 - 4x) + (24.50 - 5x) = 109.50

6(24.50) - 15x = 109.50

147 - 15x = 109.5

37.5 = 15x

2.50 = x

Answer: D

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