Question

please help

A gym has 2 kg and 5 kg weights. There are 10 disks in all. The total weight of 2 kg disks and 5 kg disks is equal to 29 kg. Find the number of disks of each kind in the gym.

a. 5 kg disk: 17; 2 kg disk: 7
b. 5 kg disk: 3; 2 kg disk: 7
c. 5 kg disk: 3; 2 kg disk: 13
d. 5 kg disk: 7; 2 kg disk: 3

Answer 1

this cannot be that hard

Answer 2

want to solve as a system of equations or some other way?

Answer 3

im not good at word problems at all I tried it and failed

Answer 4

ok lets do it a couple ways, make your teacher happy
first of all, there are ten in all, and you have 4 choices

Answer 5

okay

Answer 6

a. 5 kg disk: 17; 2 kg disk: 7
you gotta be kidding there are only 10 disks, not \(17+7=24\)!

Answer 7

c. 5 kg disk: 3; 2 kg disk: 13
not likely since \(3+13=16\)
so now we know it is either B or D

Answer 8

b. 5 kg disk: 3; 2 kg disk: 7
ok at least this one has the right number of disks, namely 10
lets compute the weight and see if we get 29 kg

Answer 9

3 5kg disks gives \(3\times 5=15\) kg and 7 2kg disks gives \(7\times 2=14\) kg and \(15+14=29\) so i guess we have to check no further

Answer 10

now we didn't actually solve the problem we just checked which answer is right
would you like to go ahead and solve it as if we did not have choices?

Answer 11

sure

Answer 12

ok we have a couple things we could do
lets call the number of 5 kg disks a variable , say \(x\)
then since the total number of disks is \(10\) then number of 2 kg disks is \(10-x\) (since they add to 10)
then the total weight would be
\[5x+2(10-x)\] which we know is \(29\) so we can solve
\[5x+2(10-x)=29\] for \(x\)

Answer 13

lets solve and see that we get \(x=3\) as predicted
remove the parentheses carefully and get
\[5x+20-2x=29\] combine like terms for
\[3x+20=29\] subtract \(20\)
\[3x=9\] and so \[x=3\] as we knew

Answer 14

okay so it would be D