A certain elevator has a safe weight limit of 2,000 pounds.

A certain elevator has a safety weight limit of 2000 pounds. Whats is the greatest possible number of people who can safely ride on the elevator at one time with the average (aritmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?

A. 7
B. 8
C. 9
D. 10
E. 11

.5X(180)+.5X(215)<=2000
X<=~10.125
Greatest possible integer is 10

So--D

x/2(180) + x/2(215) = 2000

That gives x = (2000 * 2)/395, x ~ 10.1

So it has to be D

2000 pounds total

180*x/2 + 215*x/2 = 2000

Max is 10

Hence D

Hope it helps
Cheers!
J

wow, you saves a lot of time with your brilliant method

10 people.

Equation to use: --> (#/2)(180)+(#/2)(215) = CANNOT EXCEED 2,000

5(180)+5(215) = 1975 [We've maxed out on this option, thus this is correct]

Alternative Approach :

People can not be divided in half..... so we remove odd options . Remaining with 8 & 10.
Start with the largest :10: so 5*180 +5 * 215=900+1075=1975<2000.
Hence, Ans is 10 (D)

Gladiator59

how did we get this ? \(\frac{180x}{2}\)and this \(\frac{215x}{2}\)


I understand that average weight of half group is 180 , and average weight of another one is 215

but why do we divide by 2 ; we dont know number of persons in each group right

thanks!

dave13, So let n folks have an average weight of 180 pounds ... total weight will be 180n.

The other n will have average wt of 215, so total weight will be 215n

Now, the total weight of the entire group will be 215n + 180n = 395n

whereas total no. of folks will be 2n... so the new average will be = 395n/2n = 395/2 = 197.5

That's how we get the divide by 2

Hope it is clear.

best,
Gladi

Now as we see that average weight of two groups is divided in half, then only even values will work.

Said that out of 8 and 10,only 10 will work

(180 + 215)/2 = 197.5

Since we will get 1975 as the sum, which when divided by 10, gives us the average as 197.5

Since the correct answer will include two equal numbers of people, and since people do not come in fractional quantities and, thus, may be represented only by integer values, the correct answer will be the sum of two equal integer values, and thus, must be an even number.

So, the only two choices that work are (B) 8 and (D) 10.

While the riders may have various weights, we can ignore the variation in the weights because we know that the average weight of half of the riders is 180 pounds and the average weight of the other half of the riders is 215 pounds. So, we can proceed as we would if half the riders weighed exactly 180 pounds each and the other half weighed exactly 215 pounds each.

Since the average rider weight of half of the riders is 180 pounds, and the average rider weight of other half of the riders is 215 pounds, the average rider weight of all the riders is the average of these two numbers.

We can see that, because 180 is 20 less than 200, 215 is 15 greater than 200, and 20 > 15, the average rider weight is under 200 pounds.

Thus, 10 riders can ride, as 10 x (a number < 200) < 2000.

The correct answer is (D).

let x is the total number of people that can be accommodated

x/2* 180 + x/2*215= 2000
395(x)/2=2000 >> 395(x)=4000>> x= 4000/395= 800/79

the question asks "approx" no. of people. make your life easier. 79 is approx equal to 80

800/80= 10 people (approx)

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