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31 May 2026, 08:22
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When they lived alone, Ada used one standard-sized box of Clover laundry detergent every 20 weeks, and Pablo used one standard-sized box every 8 weeks. After they began living together, their total detergent usage decreased by 90 grams per week. If they now use one standard-sized box every 10 weeks, what is the net weight of a standard-sized box of Clover laundry detergent?
(A) 600 grams
(B) 750 grams
(C) 875 grams
(D) 1,000 grams
(E) 1,200 grams
(A) 600 grams
(B) 750 grams
(C) 875 grams
(D) 1,000 grams
(E) 1,200 grams
31 May 2026, 08:46
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Quite a tricky problem.
Firstly we need to convert it into work/rate problem properly.
Every week the two of them would use up:
1/20+1/8 = 7/40*x worth of detergent per week.
Now we know that the usage decreases by 90 per week.
Which means that the amount of detergent saved is 90*10 = 900 over the course of the time.
How much time? Stem says they use it once after 70 days, or 10 weeks.
Now with a rate of 7/40 per week -> Number of weeks to complete the detergent = 40/7.
There is an addtion -> 10 - 40/7 = 30/7 days.
We have an additional 30/7 days that the detergent lasts because we saved 900grams in total.
Thus 30x/7 = 900
x = 210.
210 grams of detergent is used per week.
Now we know from the first part that 7/40 of work is done per week.
Thus 7x/40 = 210
x = 1200.
1200 grams of detergent in total is being used by them.
Firstly we need to convert it into work/rate problem properly.
Every week the two of them would use up:
1/20+1/8 = 7/40*x worth of detergent per week.
Now we know that the usage decreases by 90 per week.
Which means that the amount of detergent saved is 90*10 = 900 over the course of the time.
How much time? Stem says they use it once after 70 days, or 10 weeks.
Now with a rate of 7/40 per week -> Number of weeks to complete the detergent = 40/7.
There is an addtion -> 10 - 40/7 = 30/7 days.
We have an additional 30/7 days that the detergent lasts because we saved 900grams in total.
Thus 30x/7 = 900
x = 210.
210 grams of detergent is used per week.
Now we know from the first part that 7/40 of work is done per week.
Thus 7x/40 = 210
x = 1200.
1200 grams of detergent in total is being used by them.
kevincan
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