Difference between revisions of "2007 iTest Problems/Problem 26"
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Julie runs a website where she sells university themed clothing. On Monday, she sells thirteen Stanford sweatshirts and nine Harvard sweatshirts for a total of $370. On Tuesday, she sells nine Stanford sweatshirts and two Harvard sweatshirts for a total of $180. On Wednesday, she sells twelve Stanford sweatshirts and six Harvard sweatshirts. If Julie didn't change the prices of any items all week, how much money did she take in (total number of dollars) from the sale of Stanford and Harvard sweatshirts on Wednesday? | Julie runs a website where she sells university themed clothing. On Monday, she sells thirteen Stanford sweatshirts and nine Harvard sweatshirts for a total of $370. On Tuesday, she sells nine Stanford sweatshirts and two Harvard sweatshirts for a total of $180. On Wednesday, she sells twelve Stanford sweatshirts and six Harvard sweatshirts. If Julie didn't change the prices of any items all week, how much money did she take in (total number of dollars) from the sale of Stanford and Harvard sweatshirts on Wednesday? | ||
| − | == Solution == | + | |
| + | ==Solution== | ||
| + | |||
| + | Let <math>s</math> be cost of Stanford clothing, and let <math>h</math> be cost of Harvard clothing. From the given information, | ||
| + | <cmath>13s + 9h = 370</cmath> | ||
| + | <cmath>9s + 2h = 180</cmath> | ||
| + | Add the two equations to get | ||
| + | <cmath>22s + 11h = 550</cmath> | ||
| + | Multiply both sides by <math>\frac{6}{11}</math> to get | ||
| + | <cmath>12s + 6h = 300</cmath> | ||
| + | Thus, Julie earns <math>\boxed{\$300}</math> on Wednesday. | ||
| + | |||
| + | ==See Also== | ||
| + | {{iTest box|year=2007|num-b=25|num-a=27}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 18:12, 10 June 2018
Problem
Julie runs a website where she sells university themed clothing. On Monday, she sells thirteen Stanford sweatshirts and nine Harvard sweatshirts for a total of $370. On Tuesday, she sells nine Stanford sweatshirts and two Harvard sweatshirts for a total of $180. On Wednesday, she sells twelve Stanford sweatshirts and six Harvard sweatshirts. If Julie didn't change the prices of any items all week, how much money did she take in (total number of dollars) from the sale of Stanford and Harvard sweatshirts on Wednesday?
Solution
Let 
be cost of Stanford clothing, and let 
be cost of Harvard clothing. From the given information,
![\[13s + 9h = 370\]](http://latex.artofproblemsolving.com/3/2/7/327814afbfdfbfea231d9a2fe03924f5350ea834.png)
![\[9s + 2h = 180\]](http://latex.artofproblemsolving.com/a/7/a/a7a2b40749f60fe7b0c34bba050fb801a8beeb85.png)
Add the two equations to get
![\[22s + 11h = 550\]](http://latex.artofproblemsolving.com/9/c/a/9ca98a018b7380d71bdbe6d174185b8860b93ebc.png)
Multiply both sides by 
to get
![\[12s + 6h = 300\]](http://latex.artofproblemsolving.com/e/d/d/eddcc86601b066fc35d82199658cc8c2aea8855f.png)
Thus, Julie earns 
on Wednesday.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 25 |
Followed by: Problem 27 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
