Question

4 coffees and 12 lattes. Costs $61

12 coffees and 7 lattes. Costs $59.75
How much does a coffe and a latte cost

Answer 1

Cost of a coffee is $2.5 and cost of a latte is $4.25.

Explanation:

Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.

Given:

4 coffees and 12 lattes cost $61.

12 coffees and 7 lattes cost $59.75.

∵ 1 coffee cost =
`c`

∴ 4 coffees cost =
`4c` and 12 coffee cost =
`12c`

∵ 1 latte cost =
`l`

∴ 12 lattes cost =
`12l` and 7 lattes cost =
`7l`

Now, as per question:

`4c+12l=61-----1\\12c+7l=59.75----2`

Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,

`-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=(-123.25)/(-29)=\$4.25`

Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,

`4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=(10)/(4)=\$2.5`

Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.