Question 695598: J, K, and A bought horse. J paid one-fourth of total cost. K paid $400 more than J and A paid $400 more than K. What was total cost of horse?
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! These problems may be confusing because of all the information we have to take into account. The best way to get these problems done is to dive right in and see where we go with it. Let's analyze each sentence of the information and see what we come up with.
"J, K and A bought a horse." This sentence is probably irrelevant unless we really need to know what kind of animal they bought. What we really need to see from this information is that there are three parts: J's part, K's part and A's part. What we need to do is find each one's part in mathematical terms.
"J paid one-fourth of the total cost." It lets us know that out of the total cost, J paid 1/4 of it. The fragment "1/4 of" translates to "1/4 times" in mathematical language (of = multiplication). So, "1/4 of total cost" could translate to 1/4(t) or t/4 (letting t = total cost of the horse). J's paid t/4 money for the horse. You could say that J = t/4 (J's part equals t/4) This is the first part.
"K paid $400 more than J..." Since we know what J paid, we can just add $400 to it and say this is what K has paid. J = t/4 (or J paid t/4), and since K paid $400 more than J, K = (t/4) + $400. This is the second part.
"...and A paid $400 more than K." Since we've established K's part is t/4 + $400 (K = t/4 + $400), we know that A's part must be ((t/4) + $400) + $400 or (t/4) + $800. Below might be a clearer explanation of how we get this:
Let's use t as the total cost of the horse, J as J's part, K as K's part and A as A's part.
J's part: 1/4 of t, which 1/4(t) = 1/4 * t/1 = t/4.
K's part: J + $400 ($400 more than J's part). Since J's part = t/4, K = (t/4) + $400.
A's part: K + $400 ($400 more than K's part). Since K's part = (t/4) + $400, A = ((t/4) + $400) + 400 or (t/4) + $800.
"What was total cost of horse?" This is the question we need to answer. Since we've said that the total cost of a horse is t, we need to solve for t. So what about the three parts above? Well, if we add them all together we get the total cost of the horse, right? J's part plus K's part plus A's part should get us what the horse cost. We then have the equation J + K + A = t. Now we just have to plug each part into the capital letters and solve for t:
J + K + A = t
(t/4) + (t/4) + $400 + (t/4) + $800 = t
3t/4 + $1200 = t (or 3/4 times t; combine like terms)
$1200 = t/4 (or 1/4 times t; subtract 3t/4 from each side)
$4800 = t (multiply each side by 4).
We have the total cost of the horse to be $4800. We could then find J's part to be $1200, K's part to be $1600 and A's part to be $2000.
A similar method would be to look at the question right off the bat. This would make solving the problem easier because we know what we need to find before we try finding it. It would make more sense to know how far we are digging before we start digging. If we looked at the question first, then we would know that we were solving for the total cost of the horse.
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