Please help us interpret these Saxon word problems.

[egao_gakari]

From Algebra 1/2 (second edition), test 33. The answer key got lost in our cross country move and I've never been able to find a 2nd edition answer key for purchase online, so I have been just calculating the answers by myself all year. But these two questions are driving us up a wall today, possibly because I am in an allergy brain fog. Or possibly because they are spectacularly poorly-worded questions?

Problem 2. "The product of a number and -7 increased by 13 is 53 more than the product of 4 and the number. What is the number?"

• My setup: -7N + 13 = 4N + 53. The answer I got was N=(-40/11)
• DD14's setup: -7N+ 13 = 4N - 53. The answer she got was N=6. This seems more like a "right answer" than the solution I came up with, but I just can't understand how you could possibly interpret the wording of the original problem in such a way that you would subtract 53 from 4N. (-7N +13) is already 53 bigger than (4N), so how would taking 53 more away from 4N make sense? She keeps trying to explain why she set it up that way, but I am so confused by her explanation that I literally can't even summarize it here.

Problem 4. "A single die is rolled three times. The first two tries are both six. What is the probability of the third try being a six?"

• My interpretation: The first two tries being six have no bearing on the probability of rolling a six on the third try. The probability is 1/6.
• DD14's interpretation: The question wants to know the probability of rolling three 6's in a row, so: (1/6)(1/6)(1/6)=(1/216)

Are these questions just so badly worded that they could legitimately be interpreted either way? If anybody happens to have the 2nd edition test answer key on hand, you could just chime in with what Saxon says are the correct answers, too. 😛 

[RKWAcademy]

*face palm*

Edited June 19, 2021 by RKWAcademy
What was I thinking?

[wendyroo]

1 hour ago, RKWAcademy said:

For your first one, the -7N side is 53 higher than the 4N side so it would be plus 53 on that side so -53 on the other side. Sorry your dd is correct. Wow that explanation is hard to type. 
(-7N +13) is 53 more than 4N

The two sides would be equal if not for the fact that the left side is 53 more. So you could add 53 to the left or subtract from the right. 
 

The more I attempt an explanation, the worse it gets. 

I don't agree at all.

Think about this example:
The product of 10 and 2 increased by 5 is 13 more than the product of 4 and 3.
You can easily verify through simple arithmetic that that is a statement of fact.
We would write it: 10 * 2 + 5 = 13 + 4 * 3
Clearly we could not subtract the 13 from the right-hand side and still end up with a true equation.

Or this simpler example:
The number of quarters Dan has is 3 more than the number Mark has.
D = 3 + M
This only makes sense. If Dan has 10, then Mark has 7...because Dan has 3 more. So you have to add the 3 to Mark's number.

In the original problem, -7N + 13 = 4N + 53, if you subtract the 53 on the right, or add it on the left, then you are saying that (-7N + 13) needs more added to it in order to be as big as 4N. But the problem tells us that -7N + 13 is already 53 more than 4N. So, just like Dan and Mark's quarters, you have to add 53 to the smaller quantity in order to make the equation balance. -7N + 13 is 53 more than 4N, so if you add 53 to 4N then it will be equal to -7N + 13.

[daijobu]

Problem 2

@RKWAcademy is incorrect.  This is the equation:

So solving for  we get

"is" means equals.  If an expression "is  more" than another quantity, then that expression "equals  plus" that quantity.  

Just because it ain't an integer doesn't mean it ain't right.  

 

Edited June 19, 2021 by daijobu

[daijobu]

Problem 4

Dice have no memory.  If the problem is asking given a die has already been rolled and those rolls were both 6, that die has no preconceived notions of what it's next roll should be.  That probability is still .

Your dd is telling you the probability that one rolls three 's in a row, which is different from just rolling one .  

[kiwik]

On 6/19/2021 at 3:05 PM, daijobu said:

Problem 4

Dice have no memory.  If the problem is asking given a die has already been rolled and those rolls were both 6, that die has no preconceived notions of what it's next roll should be.  That probability is still .

Your dd is telling you the probability that one rolls three 's in a row, which is different from just rolling one .  

This is true but in all likelihood they want to know what the daughter worked out unless Saxon is known for trick questions.  

If I was asked if in a test I would say "in any throw of a fair did the probability of getting a 6 is 1/6, however the probability of getting 3 sides ..."