Hello,

I was hoping you could help me solve the problem on page 119 in book 10 using the number-line strategy.

I understand that Brand Q is closer to 15 than Brand P. However beyond that step-I'm lost.

Thanks

Here is the correct approach:

P = amount of brand P
Q = amount of brand Q

64 = P + Q ... total amount of mix

15 = .20P + .25Q ... amount of almonds in the mix


64 = P + Q
15 = .20P + .25Q


64 = P + Q
1500 = 20P + 25Q


1280 = 20P + 20Q
1500 = 20P + 25Q


- 220 = -5Q

Q = 220/5 = 44


- Veritas Help

Thank you, however the response did not answer my question.

I am interested in using the number-line strategy that is highlighted earlier in the book. Again I understand that brand Q is closer to 15 than Brand P. Its the following steps that I am unsure of.

if we had all P: 64 * .2 = 12.8

If we had all Q: 64 * .25 = 16

Since 15 is closer to 16 than it is to 12.8, the mixture must have more Brand Q than Brand P, so that rules out choices A, B, and C


if we try choice E, we get: 16*.2 + 48 * .25 = 3.2 + 2 = 15.2, so the correct answer must be D

My apologies, I will be more specific with my questions.

I understand that Brand Q is closer to 15.

My question corresponds to the next step after we discover that Brand Q is closer to 15. Why does this information (Brand Q being closer to 15) mean that choices A, B, C are ruled out. Additionally where does the 48 come from? Is the number-line strategy mainly used for questions that require ratio answers?

Also I think that 3.2 + 12= 15.2 The pre-written response for this problem contains an error, as it shows only 2 and not 12. You may want to update this in the pre-written answers that are sent out in response to email and forum questions.

The number line strategy is much more useful when we don't have something with 64 potential steps spread over a range of only 5 percentage points...
I.e. - if we had 64 percentage points - where one was 20% nuts and the other was 84% nuts, then we'd be more able to apply the number line strategy here --
As it is, we have 5 percentage points.
If we had equal amounts of P and Q, (32 oz each) then we'd have 22.5% nuts in the final mix. Since we have 15/64 of the final mix almonds, which is roughly 23%. This means we must have more of the mix that contains 25% almonds than the mix that has 20% almonds.

Here's the concept:
The higher the proportion of the 25% mix we have, the higher the proportion of almonds in the final mix, and at the extreme end, if we have 100% of Brand Q, then we have 25% almonds in the final mixture. If, on the other hand, we have 100% of Brand P, then we have 20% almonds in the final mixture. Since our final mix is about 23%, we know that this is skewed closer to 25% than to 20%, telling us we have slightly more of Brand Q than of Brand P.

Hope this helps a bit -
Apologies for the typo - we don't use pre-written answers on these, so occasionally we make a typo in our calculations. We do our best to catch these, but one slips through from time to time. Hopefully, it doesn't detract from the explanation itself or the concepts presented.

Veritas Help

Great! Thanks for the explanation!