Julia spends 5/9 of her money on a flan and two chicken pies. Each chicken pie costs 1/6 as much as the flan. Julia has $24 left.

Question

How much does Julia spend?

how much does the flan cost?

 

please do step by step calculations?

Answer 1

Let's start by calling the necessary variables.

 

X = amount of money Julia has.

C = cost of chicken pie

F = cost of flan

 

We know from the first statement that:

 

5/9*X = F + 2*C

 

This is stating that 5/9 of Julia's total money equals the cost of flan plus the cost of 2 chicken pies.

 

We also know that:

 

C = 1/6*F

 

This says that the cost of the flan is 1/6th the cost of chicken pie.

 

Finally, we know that:

 

X - 5/9*X = 24

 

This means that whatever Julia started off with, minus what she spent, is equal to $24.

 

So you have 3 equations and 3 unknowns:

 

5/9*X = F + 2*C

C = 1/6*F

4/9*X = 24

 

From the third equation:

 

X = 24*9/4 = $54

 

From the second equation:

 

5/9*54 = F + 2*C

30 = F + 2*C

 

C = 1/6*F

30 = F + 2*(1/6*F)

30 = F + 1/3*F

30 = 4/3*F

 

F = $22.50

 

Julia started off with $54.

She spent $30.

The flan was $22.50.

 

**

 

Always good to check your results.

 

What she spent should be 5/9 of what she started with:

 

30 = 54*5/9. Check.

 

If a flan was $22.50, and she spent $30, that means she spent $30 - $22.50 = $7.50 on the 2 pies, meaning the pies were $3.75 each.

 

$3.75 should be 1/6 of $22.50.

 

$22.50/6 = $3.75. Checkmate.

 

Hope this helps.