Word Problem: a ball and a bat cost 4000 USD together....

[Lenny43]

The question says a ball and a bat cost 4000 USD together. The shop sold the bat at a profit of 30% and the ball at a loss to 15% for 4500. Find the cost of the individual items. I don't know how to approach this problem.

 

[tkhunny]

The question says a ball and a bat cost 4000 USD together. The shop sold the bat at a profit of 30% and the ball at a loss to 15% for 4500. Find the cost of the individual items. I don't know how to approach this problem.

#1 - And this is about half of what it takes to solve such things - NAME STUFF!
L = cost of the ball
T = cost of the bat

There! Now, we can talk about them.

#2 - Translate sentences based on these new names.

"..ball and bat cost 4000 USD together." ==> L + T = 4000 USD

Can you express "ball at 30% profit" using the name "L"?
Do the same for the bat.
You're almost done!

 

[Lenny43]

I worked out the naming part but not sure how to proceed,

L+T=4000 and
(L+30%)+(T-15%)= 4500

what next?

 

[Deleted member 4993]

I worked out the naming part but not sure how to proceed,

L+T=4000 and
(L+30%)+(T-15%)= 4500

what next?

The second equation should be:

L*(1+0.30) + T*(1-0.15)= 4500

Do you see why?

 

[Lenny43]

The second equation should be: L*(1+0.30) + T*(1-0.15)= 4500 Do you see why?

Makes more sense that way, thanks. Now we're stuck with 1.3L+0.85T=4500 though. I just can't see a way to eliminate either L or T to get one of them.....

 

[tkhunny]

Makes more sense that way, thanks. Now we're stuck with 1.3L+0.85T=4500 though. I just can't see a way to eliminate either L or T to get one of them.....

You still have L + T = 4000, or L = 4000 - T.

Seeing any way to proceed?

 

[sinx]

I worked out the naming part but not sure how to proceed,

L+T=4000 and
(L+30%)+(T-15%)= 4500

what next?

Khan's explanation, a little different
L=cost of the ball ($)
T=cost of the bat ($)

eqn 1; L+T=$4000
eqn 2; (L+30%)+(T-15%)= 4500
you have the right idea, but

in the second eqn; (L+30%) needs to be (L+0.30L); or 1.3L
[do the same for T]
You are right, the sale is 30% over cost, but the sale amount = the cost+30% of the cost.
also, the 30% over has to be in the same units as the cost, dollars.
this last part will help you not mess up in the future. [you can't add % to $, you have to add $ to $; 'apples to apples'.]

eqn 2; 1.3L+0.85T= $4500;

now solve L+T=$4000 for L, (or T), plug the value into eqn 2, and you are almost there.

 

[Lenny43]

L= $4000-T

Using L in the second equation
1.3(4000-t)+0.85T= $4500

T= 1555.

It's so simple! Just writing it in the proper manner is 90% of the problem. Thanks a lot everyone!

 

[Steven G]

I worked out the naming part but not sure how to proceed,

L+T=4000 and
(L+30%)+(T-15%)= 4500

what next?

You never add 30% or subtract 15%. You add 30% of something and subtract 15% of something! Think what 55 + 30% would equal. It makes no sense at all!

You need to take 30% of L and 15% of T. So the 2nd equation becomes (as already mentioned) (L+.30L) + (T-.15T) = 4500