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Agatha asked in Math

Need help with this question

Thank You
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Pragati Bhatia answered this

Dear student,
Let number of cakes be x
Number of muffins be 2x
Let Cost of 1 cake be $y
Cost of 1 muffin be $(y-0.80)
Total amount spent on x cakes = $xy
Total amount spent on 2x muffins = $2x(y-0.80)
ATQ    
total cost spent on muffins = total cost spent on cakes + 19.20
2x(y-0.80) = xy + 19.20
2xy - 1.60x = xy + 19.20
xy - 1.60x - 19.20 = 0                                                          -(1)
Also, xy + 2x(y-0.80) = 96
xy + 2xy - 1.60x = 96
3xy - 1.60x - 96 = 0                                        -(2)
Multiply (1) by 3 and then subtract from (2)
[3xy - 1.60x - 96] - [3xy - 4.80x - 57.60] = 0
3xy - 1.60x - 96 - 3xy + 4.80x + 57.60 = 0
3.20x - 38.40 = 0
x = 12
put value in (1) to get y
xy - 1.60x - 19.20 = 0 
12y - 19.20 - 19.20 = 0
12y - 38.40 = 0
y = 3.20
cost of 1 cake = $3.20

Regards