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

Answer:

Grand coffee cup = 1469 gm

Jumbo coffee cup = 60 gm

Step-by-step 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.

$23x = 36846-51y$

$x=\frac{36846}{23}-\frac{51}{23}y$

$x=1602-\frac{51}{23}y$ ---------(3)

Substitute $x=1602-\frac{51}{23}y$ in equation 2.

$58(1602-\frac{51}{23}y)+68y=59460$

$92916-\frac{51\times 58}{23}y+68y=59460$

$-\frac{2958}{23}y+68y=59460-92916$

$\frac{-2958+1564}{23}y=-33456$  

$\frac{-1394}{23}y=-33456$

Using cross multiplication.

$y=\frac{-23\times 33456}{-1394}$

$y = 55.99$

y ≅ 60 gram

Substitute y = 60 in equation 3.

$x=1602-\frac{51}{23}\times 60$

$x=1602-\frac{3060}{23}$

$x=1602-133.04$

$x = 1469$ grams

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