Question

Alejandro has 3 times as many $20 bills in his wallet as he has $5 bills. He also has twice as many $1 bills than $20 bills. If he has a total of $142 in his wallet, how much money does Alejandro have in $1 bills?

Answer 1

@phi

Answer 2

give a name to the number of $1 bills. (that is what you want to find)

Answer 3

c ?

Answer 4

is it fine to have a variable for each of the bills?
$20 bills = a
$5 bills = b
$1 bills = c

Answer 5

I thought that I can make three equations
3a = b
2c = a
a + b + c = $142

Answer 6

yes, that is ok. But we have to "get rid" of the other 2 variables at some point.


a + b + c = $142

rethink that.

Answer 7

you have to keep it clear. a is the # of 20 dollar bills. (that is different from the # of dollars)

Answer 8

in other words, the amount of money is the # of bills times how much each bill is worth

Answer 9

okay so how can i change the third one?

Answer 10

think about a simpler problem and try to get that correct
say you had "a" 20 dollar bills
and the total dollars you have is 20

would you say a=20 ?

Answer 11

would i say it as 20a -> 20(20) ?

Answer 12

I'm not too clear here.

you have 1 $20 bill

but we don't know it's 1 bill. instead we are told we have "a" bills and the total dollars is 20

Answer 13

we would say the amount of money is 20a
and that equals 20
20a= 20
(and we solve for a to get 1 , the number of bills)

in your equation
a+b+c= 142

a+b+c is the number of bills, but not the amount of money

Answer 14

and shouldn't the total equation be like
3x(20)+x(5)+2x(1)=142

Answer 15

oh sorry there should be 6x(1) instead of 2x(1)

Answer 16

I don't understand how to get the total equation. Can someone explain?

Answer 17

okay we're going to take ratios
the ration of 20 to 5 is 3 to 1 right?

Answer 18

if you had 1 20, 1 5 and 1 1
how much money do you have ?

Answer 19

$26

Answer 20

yes, but a=1, b=1 and c=1
and a+b+c= 3 not 26
how do we fix that ?

Answer 21

do we have 20a + 5b + 1c = $142?

Answer 22

yes

Answer 23

For the other equations
3 times as many $20 bills in his wallet as he has $5 bills
say he has one $5 bill, then he has 3 $20 bills
b=1 a=3
it looks like a=3b

(which is backwards from what you wrote up above: b=3a)

these type sentences are confusing, so I try to think about it the way I just posted.

Answer 24

Since I have to leave I will type the whole method.
We can approach a solution using the ratio method and from the portrayal of the question it is almost evident that they are also looking for the same method
It is stated the ratio of 20 bills to 5 bill is 3 : 1
and the ratio of 20 bill to 1bill is 1:2
We can make a unified ratio by multiplying the last ratio by 3 to get a uniform ratio
20 bill to 1 bill to 5 bill
3 : 6 : 1
Now its apparent that the ratio of the bill doesn't equate to 142 but a small fraction of it
we can write
3(20)+6(1)+1(5)=142/x (142/x being the fraction part that the ratio equate to. Note treat the dollar bill as variables.)
Now multiply the x on both sides and voila you have the equation

Answer 25

i don't know how you got a= 3b when it was b=1 and a=3 @phi

Answer 26

it's either a=3b or b=3a. if we know b is 1 and a is 3 only the first equation works