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17 Jan 2018, 14:23
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Difficulty:
(N/A)
Question Stats:
100% (01:17) correct
0%
(00:00)
wrong
based on 2
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History
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Jim spent $60 purchasing lattes and coffees for his coworkers. If lattes cost $6 and coffees cost $3, and Jim purchased two more coffees than lattes, how many total drinks did he purchase?
A) 6
B) 8
C) 10
D) 12
E) 14
Official Solution:
In setting up a word problem like this, be sure to use meaningful variables. Here your variables are lattes (which you can call L) and coffees (which you can call C).
You can set up an equation to account for the $60 total: $6 times the number of lattes plus $3 times the number of coffees will account for the $60, so 6L + 3C = 60. You can then simplify by dividing everything by 3: 2L + C = 20.
You can also set up an equation based on the fact that there were 2 more coffees than lattes. The number of coffees, C, is equal to 2 plus the number of lattes, L, so:
C = 2 + L
With two equations and two variables, you can now solve. A quick way to do that is to subtract L from both sides of the second equation:
C - L = 2
If you then multiply both sides by 2, you have:
2C - 2L = 4
Which sets up for the elimination method when you stack and add the two equations:
2C - 2L = 4
C + 2L = 20
This yields 3C = 24, so C = 8. When you plug that back in to C - L = 2, you see that L = 6, meaning that the total number of drinks is 8 + 6 = 14. Choice E is correct.
Why do you just multiply it by 2? Where does that come from and when is it appropriate to do that?
A) 6
B) 8
C) 10
D) 12
E) 14
Official Solution:
In setting up a word problem like this, be sure to use meaningful variables. Here your variables are lattes (which you can call L) and coffees (which you can call C).
You can set up an equation to account for the $60 total: $6 times the number of lattes plus $3 times the number of coffees will account for the $60, so 6L + 3C = 60. You can then simplify by dividing everything by 3: 2L + C = 20.
You can also set up an equation based on the fact that there were 2 more coffees than lattes. The number of coffees, C, is equal to 2 plus the number of lattes, L, so:
C = 2 + L
With two equations and two variables, you can now solve. A quick way to do that is to subtract L from both sides of the second equation:
C - L = 2
If you then multiply both sides by 2, you have:
2C - 2L = 4
Which sets up for the elimination method when you stack and add the two equations:
2C - 2L = 4
C + 2L = 20
This yields 3C = 24, so C = 8. When you plug that back in to C - L = 2, you see that L = 6, meaning that the total number of drinks is 8 + 6 = 14. Choice E is correct.
Why do you just multiply it by 2? Where does that come from and when is it appropriate to do that?
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17 Jan 2018, 20:54
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Discussed here: jim-spent-60-purchasing-lattes-and-coffees-for-his-coworkers-if-latt-257834.html
Please search before posting and name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
