Question

Newberg City Cafe recently introduced a new flavor of coffee. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equaled a total of 36,846 grams. The day before, 58 grande cups and 68 jumbo cups were served,which used a total of 59,460 grams. How much coffee is required to make each size?

Answer 1

Grand coffee cup = 1469 gm

Jumbo coffee cup = 60 gm

Explanation:

Let x be the grande coffee cup and y be the jumbo coffee cup.

Solution:

From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.

So, the equation is.

`23x+51y = 36846` ---------(1)

From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.

`58x+68y=59460` ----------(2)

Solve the equation 1 for x.

`23x = 36846-51y`

`x=(36846)/(23)-(51)/(23)y`

`x=1602-(51)/(23)y` ---------(3)

Substitute
`x=1602-(51)/(23)y` in equation 2.

`58(1602-(51)/(23)y)+68y=59460`

`92916-(51* 58)/(23)y+68y=59460`

`-(2958)/(23)y+68y=59460-92916`

`(-2958+1564)/(23)y=-33456`

`(-1394)/(23)y=-33456`

Using cross multiplication.

`y=(-23* 33456)/(-1394)`

`y = 55.99`

y ≅ 60 gram

Substitute y = 60 in equation 3.

`x=1602-(51)/(23)* 60`

`x=1602-(3060)/(23)`

`x=1602-133.04`

`x = 1469` grams

Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm