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For D to be the largest, it'd have to be bigger than B. To compare two fractions, we could test an inequality:

7/30 > 13/56

7*56 > 13*30

392 > 390

Success! This is true, so 7/30 IS > 13/56.

by [email protected]

Thu Dec 07, 2017 5:56 pm
Forum: Problem Solving
Topic: Which of the following fractions is the largest?
Replies: 3
Views: 3115

The trick is converting the problem to the units given. We want fifths of the mile, so 8 miles = 40 fifths of a mile.

From there, our first fifth costs $3.10 and our remaining 39 fifths cost 40¢ each. That gives us a fare of $3.10 + 39*40¢, or $18.70.

by [email protected]

Thu Dec 07, 2017 5:54 pm
Forum: Problem Solving
Topic: A certain taxi company charges $3.10
Replies: 6
Views: 3972

When we've got three groups A, B, and C with some overlap, we can say that Total = A + B + C + (people in no groups) - (people in exactly two groups) - 2*(people in exactly three groups) We're told that the total = 144, A = (144 - 100), B = (144 - 89), and C = (144 - 91). (Remember that A, B, C are ...


yeah

One last approach that's slow but almost foolproof is backsolving. I'll use two answers to show what the right answer should look like and what a wrong answer could look like. Suppose I try answer A, and make the race an hour long. If the race is 40 meters long, then A runs 40 meters, B runs 20, and...

by [email protected]

Thu Dec 07, 2017 5:18 pm
Forum: Problem Solving
Topic: Three runners A, B and C run a race with A finishing...
Replies: 4
Views: 1829

An approach with less algebra would go something like this: When A finishes the race, we know A has run D meters B has run D - 20 meters C has run D - 34 meters At this point, B has 20 meters left to go and C has 34 meters left to go . When B finishes the race, we know C still has 21 meters left to ...

by [email protected]

Thu Dec 07, 2017 5:08 pm
Forum: Problem Solving
Topic: Three runners A, B and C run a race with A finishing...
Replies: 4
Views: 1829

Let's start with a technical approach: Distance = Rate * Time We'll call t A's time to finish the race, and a, b, c the rates of the three runners. We know that D = a * t D - 20 = b * t D - 34 = c * t Now let's look at what happens after A finishes. Let's say that the time between A's finishing the ...

by [email protected]

Thu Dec 07, 2017 4:56 pm
Forum: Problem Solving
Topic: Three runners A, B and C run a race with A finishing...
Replies: 4
Views: 1829

A simple way: Start by treating the two I's as one unit grafted together. If we then arrange the "nine" letters (A, B, C, D, E, F, G, H, and II), we've got 9! arrangements, so there are 9! ways to put the I's together. But if we have no restrictions at all, we have 10!/2! ways of arranging 10 letter...


Another approach would be finding the weighted average.

If X is 20% sugar, Y is 40% sugar, and X + Y = 25% sugar, then

.2x + .4y = .25(x + y)

.2x + .4y = .25x + .25y

.15y = .05x

3y = x

We were told y = 150, so x = 3y = 3*150 = 450.


If we've got 150 gallons of solution Y, then 40% of 150, or 60 gallons of it are sugar. From here, we're adding x gallons of Solution X. 20% of that is sugar, so sugar / total = (60 + 0.2x ) / (150 + x ) is our ratio. We need that to equal 25%, or 1/4, so (60 + 0.2x) / (150 + x) = 1/4 Then just cros...


Another approach could use combinatorics: p(rotten) = (# of pairs with the rotten apple) / (total # of pairs) # of pairs with the rotten apple = 4, since the rotten apple could be paired with any of the other four apples total # of pairs = (5 choose 2) = 5!/(3! * 2!) = 10 So our ratio is 4/10, or 2/5.

by [email protected]

Thu Dec 07, 2017 4:31 pm
Forum: Problem Solving
Topic: A basket contains 5 apples of which one is rotten...
Replies: 6
Views: 2545

Another approach: p( getting the rotten apple ) + p( not getting the rotten apple ) = 1, since one of those two things MUST happen. Subtracting from both sides, we have p( getting the rotten apple ) = 1 - p( not getting the rotten apple ) and p( not getting the rotten apple ) = p(apple 1 fresh) * p(...

by [email protected]

Thu Dec 07, 2017 4:29 pm
Forum: Problem Solving
Topic: A basket contains 5 apples of which one is rotten...
Replies: 6
Views: 2545

Here's another way of thinking about it: Henry could select the rotten apple FIRST or SECOND. The probability that he selects it first = p(rotten apple) * p(fresh apple) = 1/5 * 4/4 = 1/5 The probability that he selects it second = p(fresh apple) * p(rotten apple) = 4/5 * 1/4 = 1/5 Adding those up, ...

by [email protected]

Thu Dec 07, 2017 4:27 pm
Forum: Problem Solving
Topic: A basket contains 5 apples of which one is rotten...
Replies: 6
Views: 2545

Another resurrected zombie thread - what is happening in the graveyard this week? :)

by [email protected]

Thu Dec 07, 2017 4:26 pm
Forum: Problem Solving
Topic: A gardener is going to plant 2 red rosebushes
Replies: 8
Views: 3205

Another approach (not quite as good, but you never know what's helpful!): pull the integers roots out of 1575K. √1575K => √1575 * √K => √(25*9*7) * √K => √25 * √9 * √7 *√K => 5 * 3 * √7 * √K => 5 * 3 * √7K So if √7K = an integer, we're set. If K = 7, then √7K = √49 = 7,...


Here's a trick: break 1575K into two identical square roots. For instance, say we have 36. 36 = 2 * 2 * 3 * 3 = (2 * 3) * (2 * 3) , or two identical square roots . Now let's try that with 1575K. 1575K => 25 * 63 * K => 5 * 5 * 3 * 3 * 7 * K => (5 * 3 * 7) * (5 * 3 * K) So if K = 7, we'll have two id...