6 lollies plus 3 ice creams cost £8.52. 3 ice creams plus 6 drinks cost £9.24. Find out individual cost of each item

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It is 6 times 4

To find the individual cost of each item, we can assign variables to each item and set up a system of equations based on the given information.

Let's say:
- The cost of one lolly is L in pounds.
- The cost of one ice cream is I in pounds.
- The cost of one drink is D in pounds.

Based on the given information, we can create two equations:

Equation 1: 6L + 3I = 8.52
(The cost of 6 lollies plus 3 ice creams equals £8.52.)

Equation 2: 3I + 6D = 9.24
(The cost of 3 ice creams plus 6 drinks equals £9.24.)

Now, let's solve this system of equations. We'll use the substitution method:

Step 1: Solve Equation 1 for L in terms of I:
Take Equation 1: 6L + 3I = 8.52
Rearrange it: 6L = 8.52 - 3I
Divide by 6: L = (8.52 - 3I)/6

Step 2: Substitute L in Equation 2 with its value from Step 1:
3I + 6D = 9.24
Substitute L: 3I + 6D = 9.24 becomes
3I + 6D = 9.24 - 3[(8.52 - 3I)/6]

Step 3: Simplify and solve for D:
3I + 6D = 9.24 - (25.56 - 9I)/6
Multiply both sides by 6 to eliminate the fraction:
18I + 36D = 55.44 - (25.56 - 9I)
Combine like terms:
18I + 36D = 55.44 - 25.56 + 9I
Simplify:
9I + 36D = 29.88

Step 4: Solve Equation 3 for D in terms of I:
Take the equation: 9I + 36D = 29.88
Rearrange it: 36D = 29.88 - 9I
Divide by 36: D = (29.88 - 9I)/36

Step 5: Substitute D in Equation 1 with its value from Step 4:
6L + 3I = 8.52
Substitute D: 6L + 3I = 8.52 becomes
6L + 3I = 8.52 - 3[(29.88 - 9I)/36]

Step 6: Simplify and solve for I:
6L + 3I = 8.52 - (89.64 - 27I)/36
Multiply both sides by 36 to eliminate the fraction:
216L + 108I = 306.72 - (89.64 - 27I)
Combine like terms:
135I + 216L = 306.72 + 89.64 - 27I
Simplify:
162I + 216L = 396.36

Step 7: We have two equations now:
162I + 216L = 396.36 (equation 4)
9I + 36D = 29.88 (equation 5)

We can solve this system of equations using any method, such as substitution or elimination, but here we will use substitution.

Step 8: Solve Equation 5 for D in terms of I:
Take the equation: 9I + 36D = 29.88
Rearrange it: 36D = 29.88 - 9I
Divide by 36: D = (29.88 - 9I)/36

Step 9: Substitute D in Equation 4 with its value from Step 8:
162I + 216L = 396.36
Substitute D: 162I + 216L = 396.36 becomes
162I + 216L = 396.36 - 36[(29.88 - 9I)/36]

Step 10: Simplify and solve for I:
162I + 216L = 396.36 - (1073.76 - 324I)/36
Multiply both sides by 36 to eliminate the fraction:
5832I + 7776L = 14249.76 - (1073.76 - 324I)
Combine like terms:
6156I + 7776L = 14249.76 + 1073.76 - 324I
Simplify:
6480I + 7776L = 15323.52

Step 11: To isolate I, we subtract 6480I from both sides:
6480I + 7776L - 6480I = 15323.52 - 6480I
Simplify:
1296L = 15323.52 - 6480I

Step 12: Divide by 1296 to solve for L:
L = (15323.52 - 6480I)/1296

Now we have the equations for both L and I.

To find the individual cost of each item, substitute the value of L or I back into one of the original equations.

For example, let's use Equation 1:
6L + 3I = 8.52

Substitute the value of L from Step 12 into the equation:
6[(15323.52 - 6480I)/1296] + 3I = 8.52

Simplify and solve for I:
(229853.28 - 9720I)/1296 + 3I = 8.52
Multiply both sides by 1296 to eliminate the fraction:
229853.28 - 9720I + 3888I = 11021.92
Combine like terms:
-5832I = -218831.36
Divide by -5832:
I ≈ 37.55

Now substitute the value of I back into Equation 1 to solve for L:
6L + 3(37.55) = 8.52
6L + 112.65 = 8.52
6L = -104.13
L ≈ -17.36

However, a negative value for cost does not make sense in this context. Therefore, we need to re-evaluate our calculations.

It's likely that there was an error or inconsistency in the information provided or in the calculations performed. I apologize for the confusion caused, and please double-check the given information or provide any additional details if available.