fractions and baseball cards: How many does Darlene have?

[spicylatina]

I don't know how to get started on solving this problem:

Darlene was asked how many baseball cards she owns. She said "if one fourth, one fifth, and one sixth of my collection were added together, they would total thirty seven cards.' How many baseball cards does Darlene have?

Should I get started by finding one fourth of 37?

Thank you!

 

[galactus]

Let x = the total number of cards

Then (x/4)+(x/5)+(x/6)=37

Solve for x.

 

[spicylatina]

ok so how do u solve x/4 + x/5 + x/6? do u multipy both by 37?also its 1/4, 1/5, 1/6. where does x come in?
My work:x/4 + x/5 + x/6
x/120 (do i find the common denominator which is 120?). i got x=120. so there are 120 baseball cards. is that right? what did everybody else get?

 

[Mrspi]

Re: fractions and baseball cards

ok i don't know how to get started on solving this problem: Darlene was asked how many baseball cards she owns. She said "if one fourth, one fifth, and one sixth of my collection were added together, they would total thirty seven cards.' How many baseball cards does Darlene have?
*ok so should I get started by finding one fourth of 37? I'm confused. please help!

Let x = the total number of card she has

So,

(x / 4) + (x / 5) + (x / 6) = 37

You can add the fractions on the left side, but you need to first make them all have a common denominator. The least common multiple of 4, 5, and 6 is 60. Rewrite each fraction so it has a denominator of 60:

(x*15/4*15) + (x*12/5*12) + (x*10/6*10) = 37

(15x/60) + (12x/60) + (10x/60) = 37

Add the numerators, and place the sum over the common denominator:

(15x + 12x + 10x) / 60 = 37

37x/60 = 37

Ok...now...can you take it from here?

 

[spicylatina]

um ok. except I end up getting a decimal or fraction answer. fraction:1 37/23
or I get 6.12 and on and on and on. there shouldn't be a fraction or decimal answer right?

 

[stapel]

I end up getting a decimal or fraction answer. fraction:1 37/23....

Please reply showing all of your steps, so that the tutors can see how you went from "(37/60)x = 37" to "x = 1³⁷/₂₃". (If they can't see your work, they can't find where you're making the error.)

Please be complete. Thank you!

Eliz.

 

[spicylatina]

x/4 + x/5 + x/6=37
x/4x15/15=15x/60
x/5 x 12/12=12x/60
x/6x10/10=10x/60
15x/60 + 12x/60 + 10x/60 = 37/60
37x/60=37
-23/37=1 37/23

 

[Deleted member 4993]

x/4 + x/5 + x/6=37
x/4x15/15=15x/60
x/5 x 12/12=12x/60
x/6x10/10=10x/60
15x/60 + 12x/60 + 10x/60 [= 37/60 incorrect] should be

15x/60 + 12x/60 + 10x/60 = 37 [you have simply multiplied by 1 on the other side]

37x/60 = 37

x = 60

 

[Loren]

\(\displaystyle \frac{x}{4} + \frac{x}{5} + \frac{x}{6}=37\)

In my opinion it is easier to simply multiply both sides of the equation by the least common denominator.

\(\displaystyle 60(\frac{x}{4} + \frac{x}{5} + \frac{x}{6}) = 60(37)\)

This leads to 15x + 12x +10x = 2220

Certainly you can take it from there getting x = 60?