Is there a better way to solve for this problem than how i did?

Question

At a retail store, the price for a med. shirt is 14.99 & the price for a large shirt is 19.99. Sherrie bought 10 shirts at the store and paid a total of 169.90, excluding tax. How many medium shirts did she buy?
A.3
B.4       
C.5     
D.6      
E.7                       
D is the correct answer.

However, I wasn't sure how to solve for it on the test, therefore did:
for 10 shirts total she could buy..
A: 3 @ 14.99 and 7 @ 19.99 but that = 184
B:  4 @ 14.99 and 6 @ 19.99 but that = 393
etc..
and did C which was 6 @ 14.99 and 4 @ 19.99
(6 x 14.99) + (4 x 19.99) = 169.90 therefore getting the correct answer..

However this process is lengthy/time consuming for a test, and simply plugging in answers..
Could you please explain to me a better and more efficent way to solve for this problem?
Thanks!

Melissa · Accepted Answer

Lets call the number of medium shirts as m and the number of large shirts l.
Therefore  since the total number of shirts is 10 then 10=l+m
Also since the prices were given then:
total=m(price of medium shirt)+l(price of large shirt)
So 169.90=14.99m+19.99l
Now we have two equations and two unknowns so we can solve for one and substitute in the other.
So m=10-l
Then 169.90=14.99(10-l)+19.99l
Distribute the l through: 169.90=149.90-14.99l+19.99l
Solve for l then plug back in for m

pioneers · Answer

no. of med. sh. = x 
no. of large sh. = 10 - x
14.99 x + 19.99(10 - x ) = 169.90 ....
solve for x ........
14.99 x + 199.9 - 19.99 x = 169.90
5x = 30 .... x = 6

mfratant · Answer

M+L=10

M*14.99+L*19.99=169.9

(10-L)*14.99+L*19.99=169.9
19.99*L-14.99*L=169.9-149.9
5*L=20
L=4
M=6

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Is there a better way to solve for this problem than how i did?

3 Answers