An algebra problem by Geet Singh

Algebra Level pending

A chocolate manufacturing company received an order of 400 litres of dark brown chocolate and 360 litres of white milk chocolate. It has two machines (X and Y) to make these chocolates. X takes 4 hours to make 16 litres of dark brown chocolate and 3 hours to make 9 litres of white milk chocolate. Y takes 4 hours to make 12 litres of dark brown chocolate and 3 hours to make 12 litres of white milk. If the company has to deliver the order in 93 hours, its delivery will be delayed by at least

2 \frac{ 2} {7}

2 \frac{ 5} {7}

2 \frac{ 1} {7}

2 \frac{ 4} {7}

2 solutions

Sayed Nesta
May 25, 2014

Given:::::----- 1-0rder ( 400 L "D"ark + 360 L "W"hite )... 2-machine X ----- 9 L W = 3 hrs & 16 L D =4 hrs 3-machine Y------12 L W =3 hrs & 12 L D=4hrs

Y is faster 2 make "W"hite 0rder in >>>>>

3x360 /12 = 90 hrs

>it'll b free 4 0ther 3 hrs bef0re delivery time >>> s0 it can b used als0 4 s0me 0f "D"ark 0rder

3x12 / 4= 9 L 0f "Dark" 0rder >>>

the rest is ((400 - 9 L = 391 L D )))

X machine can make 391 L D in >>>>

391 x 4 / 16 = 97.75 hrs >>>>> but the 0rder time is 0nly 93 hrs

s0 0rder'll b delayed 4 >>>> 97.75 - 93 = 4.75 hrs

meaning at least 2 5/7 ((( the biggest 0f the given ch0ices ))) ;) :D :v

Geet Singh
Mar 20, 2014

X can make 4 Ltrs of Brown Chocolate per Hour & 3 Ltrs of White Chocolate per hour. Y can make 3 Ltrs of Brown Chocolate per hour & 4 Ltrs of white Chocolate per hour. If X & Y work simultaneously to make Dark Brown & White Chocolates respectively, then they can make a total of 360 Ltrs of each in 90 Hours.Another 40 Ltrs of Dark Brown Chocolate would remain.

Both X & Y working together, can finish making this remaining 40 Ltrs in 40/7 = 5 5/7 Hours.

The Company's delivery would be delayed by

[ )90 + 5 5/7) - 93] = 2 5/7 hours.

An algebra problem by Geet Singh

2 solutions

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