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.
[tex]23x+51y = 36846[/tex] ---------(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.
[tex]58x+68y=59460[/tex] ----------(2)
Solve the equation 1 for x.
[tex]23x = 36846-51y[/tex]
[tex]x=\frac{36846}{23}-\frac{51}{23}y[/tex]
[tex]x=1602-\frac{51}{23}y[/tex] ---------(3)
Substitute [tex]x=1602-\frac{51}{23}y[/tex] in equation 2.
[tex]58(1602-\frac{51}{23}y)+68y=59460[/tex]
[tex]92916-\frac{51\times 58}{23}y+68y=59460[/tex]
[tex]-\frac{2958}{23}y+68y=59460-92916[/tex]
[tex]\frac{-2958+1564}{23}y=-33456[/tex]
[tex]\frac{-1394}{23}y=-33456[/tex]
Using cross multiplication.
[tex]y=\frac{-23\times 33456}{-1394}[/tex]
[tex]y = 55.99[/tex]
y ≅ 60 gram
Substitute y = 60 in equation 3.
[tex]x=1602-\frac{51}{23}\times 60[/tex]
[tex]x=1602-\frac{3060}{23}[/tex]
[tex]x=1602-133.04[/tex]
[tex]x = 1469[/tex] grams
Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm
