Math real life problem?

anonymous

In a shop there are no prices up, but if Tom is charged 2.80AED for 3 cakes and 2 cups of Tea and Andy buys 4 cakes and 4 cups of tea for 4.60AED, how much does 1 cup of tea and 1 cake cost?

the-me

Let x be the price of a cake

let y be the price of a cup of tea.

3x+2y=2.80

4x+4y=4.60

Divide the bottom equation by -2

-2x-2y=-2.30

Add it to the first equation

3x+2y=2.80

-2x-2y=-2.30

__________

x=.50

Plug that in and find y

3(.50)+2y=2.80

1.50+2y=2.80

2y=1.30

y=.65

Cake is .50

Tea is .65

Check the answer

3(.50)+2(.65)=2.80

4(.50)+4(.65)=4.60

adam-hunt_60a3b1a89842c

"Tom is charged 2.80 for 3 cakes and 2 cups of Tea"

Let c and t be the prices for a cake and a cup of tea, respectively.

3c + 2t = 2.80

"Andy buys 4 cakes and 4 cups of tea for 4.60"

4c + 4t = 4.60

Solve the system for c and t.

Note that B's answer is incorrect. Cake and tea must cost less than 1AED each.

c = 0.50AED

t = 0.65AED

ian-collins_60a3b1a94e97c

Cake is 1.07 tea is 1.05