Ada used one standard-sized box of Clover laundry detergent

Question

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

Adit_ · Answer

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.

TangyStem · Answer

Ada uses 1x/20 of box per week, Pablo uses 1x/8 of box per week. However, since they live together, they use 90g less than their individual use combined, resulting in using 1x/10 of the box per week.
1x/20 + 1x/8 -90 = 1x/10. 
solve, x equals 1200.

LL132 · Answer

1. Before living together: 
 
 Ada's weekly use = B / 20 
 Pablo's weekly use = B / 8 
 Total combined usage before = B/20 + B/8 = 7B / 40  
 2. After living together: 
 
 They use 1 box every 10 weeks, so weekly use = B / 10 
 To keep the denominators the same, B / 10 = 4B / 40  
 3. Set up the equation:  The problem says their usage dropped by 90 grams per week.
Before - After = 90 7B/40 - 4B/40 = 90 3B/40 = 90 3B = 3600 B = 1200 grams. (E)

ReetArora · Answer

Going by options helps! ,
Let total be 1200 g 
Firstly Ada Uses 1200/20 = 60 g per week, Pablo uses 1200/8 = 150 g per week. Total =210 g . Reduced by 90 g now. so Now combined they use 210-90 = 120 . In how many weeks i.e. 1200 / 120 = 10 weeks, same is mentioned in question. Hence Answer 1200 g

The_ashura · Answer

1. Define Box Weight: Let x be the total grams in one standard box.
2. Calculate Old Combined Rate: Ada (x/20) + Pablo (x/8) = 7x/40 grams per week.
3. Calculate New Combined Rate: Together they use x/10 = 4x/40 grams per week.
4. Set Up Difference Equation: Old Rate - New Rate = 90 -> (7x/40) - (4x/40) = 90.
5. Solve for x: 3x/40 = 90 -> 3x = 3600 -> x = 1200 grams.

Option E.

MehakKaushal · Answer

Box Weight: Let x be the total grams in one standard box
Rate of ada: x/20, rate of Pablo: x/8
its given their total detergent usage decreased by 90 grams per week which means if they would have lived separately they have consumed individually= x/20 and x/8 total = x/20 +x/8. This total decreases by 90 so the equation setup is as follows
x/(x/20 + x/8 - 90) =10 
solve for X =1200

Ada used one standard-sized box of Clover laundry detergent

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Ada used one standard-sized box of Clover laundry detergent

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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