Identify Correct Equation

[harpazo]

Haley earns $9.75 per hour babysitting for 2 children. Which equation correctly relates Haley's total earnings, t, to the number of hours she
babysat, h?

A. t = 9.75h
B. h = 9.75t + 2
C. t = 9.75h + 2
D. t = 2(9.75 + h)

Solution

It is definitely not choice B. Choice D is tricky but incorrect. Let's say she worked for 2 hours. I multiply 9.75 times 2 to get 19.50. Adding 2 to 19.50 does not provide the amount she makes for babysitting two children. So, my answer is choice A.

 

[Dr.Peterson]

I'm not sure why you considered D at all. Is there any reason to add the fee per hour to the number of hours?

If you just start with the problem rather than the choices, then A should be obvious. (Wrong choices are called "distractors"; if you avoid looking at them unless necessary, you can avoid distraction!

In reading the problem, you should see that the number of children is irrelevant, so any answer including the 2 is likely to be a distractor. Then if you just think how you would calculate the fee, you realize you multiply the fee per hour by the number of hours, which leads directly to A.

 

[harpazo]

I'm not sure why you considered D at all. Is there any reason to add the fee per hour to the number of hours?

If you just start with the problem rather than the choices, then A should be obvious. (Wrong choices are called "distractors"; if you avoid looking at them unless necessary, you can avoid distraction!

In reading the problem, you should see that the number of children is irrelevant, so any answer including the 2 is likely to be a distractor. Then if you just think how you would calculate the fee, you realize you multiply the fee per hour by the number of hours, which leads directly to A.

I think MOST WORD PROBLEMS are worded poorly.

 

[Dr.Peterson]

I think MOST WORD PROBLEMS are worded poorly.

I didn't say this one was worded poorly! It's worded so as to catch students who aren't thinking, just guessing (in this case, based on wanting to use all the numbers in the problem).

And the truth is that most word problems are READ poorly!

 

[harpazo]

I didn't say this one was worded poorly! It's worded so as to catch students who aren't thinking, just guessing (in this case, based on wanting to use all the numbers in the problem).

And the truth is that most word problems are READ poorly!

This topic is open for interpretation and discussion.

 

[HallsofIvy]

Haley earns $9.75 per hour babysitting for 2 children. Which equation correctly relates Haley's total earnings, t, to the number of hours she
babysat, h?

Use "dimensional analysis" (which is just a fancy way of saying "check the units").
There are four values with units here:
9.75 dollars/hour
2 children
h hours
t dollars.

A. t = 9.75h

9.75 dollars per hour times h hours give 9.75h dollars. At least the units are correc

B. h = 9.75t + 2

9.75 dollars per hour times t dollars has unit of "dollars squared per hour" (whatever that means) and you can't add "2 children" to that!

C. t = 9.75h + 2

9.75 dollar per hour times h hours has units of dollars, which at least make sense, but still, you can't add "dollars and children"!

D. t = 2(9.75 + h)

You can't add "dollars per hour" and "hours"! They have different units.

Solution

It is definitely not choice B. Choice D is tricky but incorrect. Let's say she worked for 2 hours. I multiply 9.75 times 2 to get 19.50. Adding 2 to 19.50 does not provide the amount she makes for babysitting two children. So, my answer is choice A.

 

[harpazo]

Use "dimensional analysis" (which is just a fancy way of saying "check the units").
There are four values with units here:
9.75 dollars/hour
2 children
h hours
t dollars.


9.75 dollars per hour times h hours give 9.75h dollars. At least the units are correc


9.75 dollars per hour times t dollars has unit of "dollars squared per hour" (whatever that means) and you can't add "2 children" to that!


9.75 dollar per hour times h hours has units of dollars, which at least make sense, but still, you can't add "dollars and children"!


You can't add "dollars per hour" and "hours"! They have different units.

Thank you for the breakdown.