Some Panama hats bought in Columbia coast $24 each, and others coast $12 each. If 18 hats of these two grades coast $336 how many hats of each kind were bought?

Question

I'm not good with sentence problems.

Answer 1

Let x = # $24 hats

Let y = # $12 hats

 

we bought 18 hats so:

x+y=18 ...  equation 1

 

the money spent will be

24x + 12y

we spent $336 so:

 

24x + 12y = 336 ... equation 2

 

note that each term in equation 2 is

divisible by 12 so we can reduce it.

12(2x + y) = 12(28)

2x + y = 28 ... equation 2

 

we have 2 equations and 2 unknowns

 

x + y = 18     equation 1

2x + y = 28   equation 2

---------------  subtract equation 1 from equation 2

x = 10

 

x+ y = 18

10+y=18

y= 8

 

He bought 10 of the $24 hats

and 8 of the $12 hats

 

check answer:

24(10) + 8(12) = 336

240 + 96 = 336

336 = 336

equation balances, answer is correct.