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- #1

#### paulmdrdo

##### Active member

- May 13, 2013

- 386

let

$x$= number of quart jugs

$2x=$ number pint jugs

$x-8$ = number of gallon jugs.

can you help me how i will set up my equation?

- Thread starter paulmdrdo
- Start date

- Thread starter
- #1

- May 13, 2013

- 386

let

$x$= number of quart jugs

$2x=$ number pint jugs

$x-8$ = number of gallon jugs.

can you help me how i will set up my equation?

- Admin
- #2

- Jan 29, 2012

- 1,151

You will, of course, need to know how many pints there are in gallon and how many quarts in a gallon.

- Mar 1, 2012

- 249

Your equations are set up well. The next step would be to make sure your units are all the same - for this exercise I would recommend using pints.

let

$x$= number of quart jugs

$2x=$ number pint jugs

$x-8$ = number of gallon jugs.

can you help me how i will set up my equation?

Can you work out from the information given how many pints there are in a quart and how many pints in a gallon?

- Thread starter
- #5

- May 13, 2013

- 386

i will use the unit of gallons here

$x=$ number of quart jugs

$2x=$ number pint jugs

$x−8$= number of gallon jugs

using the given information i'll have

$\frac{1}{4}x=$ # of quart jugs(in gallons)

$\frac{1}{4}x=$ # of pint jugs(in gallons)

$\frac{1}{4}x-8=$ # of gallon jugs.

setting my equation,

$\frac{1}{4}x+\frac{1}{4}x+\frac{1}{4}x-8=22$

$\frac{3}{4}x=30$

$3x=120$ then, $x=40$

now i have,

$40$ quart jugs. converting it to gallons i'll have 10 gallons.

$80$ pint jugs equivalent also to 10 gallons.

$40$quartz-8= $(10-8)$gallons = 2 gallons

10gallons+10gallons+2gallons=22 gallons.

i think i got it right. but can you give me comment on my solution.

- Thread starter
- #6

- May 13, 2013

- 386

i also tried solving by choosing unknown represent $x=$# gallons jug and this is what i get,

$x=$# of gallon jug.

$x+8$=# of quart jug ---> convert to gallons

$2x+16=$#of pint jug----> convert to gallons

then,

$x=$# of gallon jug

$\frac{1}{4}x+2=$#of quart jug(in gal.)

$\frac{1}{4}x+2=$# pint jug (in gal.)

$x+\frac{1}{4}x+2+\frac{1}{4}x+2=22$

$\frac{2}{4}x+x+4=22$

$x=12$

now there is 12 gallon jug, 5 gallon jug(20 quart jug), 5 gallon jug(40 pint jug).

12+5+5= 22 gallons. the total gallons matches. but the individual gallons doesn't conform with my solution above. which one is correct? please help!

- Admin
- #7

Using your variables, I then obtained the following equation:

let

$x$= number of quart jugs

$2x=$ number pint jugs

$x-8$ = number of gallon jugs.

can you help me how i will set up my equation?

\(\displaystyle \frac{2x}{8}+\frac{x}{4}+x-8=22\)

\(\displaystyle \frac{3x}{2}=30\)

\(\displaystyle x=20\)

Hence, there are 40 pint jugs, 20 quart jugs, and 12 gallon jugs.

- Thread starter
- #8

- May 13, 2013

- 386

how do you get these terms $\displaystyle \frac{2x}{8}+\frac{x}{4}+x-8$

and also, can you pin point what's my mistake in my first and 2nd solution. thanks!

Last edited:

- Admin
- #9

How many pints are in a gallon? How many quarts?how do you get these terms $\displaystyle \frac{2x}{8}+\frac{x}{4}+x-8$