SOLUTION: i need help with this problem its asking to make an system of equation. "juanita and keenan own a camping supply store and just put in an order for flashlights and sleeping bags.

Question 1113275: i need help with this problem its asking to make an system of equation.
"juanita and keenan own a camping supply store and just put in an order for flashlights and sleeping bags. the number of flashlights ordered was five times the number of sleeping bags. the flashlight cost $12 each and the sleeping bag cost $45 each. if the total cost for the flash light and sleeping bag was $1784, how many flashlights and sleeping bags did they order.
thank you
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f = number of flash lights.
s = number of sleeping bags.

f = 5 * s

12 * f + 45 * s = 1784.

since f = 5 * s, replace f with 5 * s in 12 * f + 45 * s = 1784 to get:

12 * (5 * s) + 45 * s = 1784.

simplify to get 60 * s + 45 * s = 1784.

combine like terms to get 105 * s = 1784.

solve for s to get s = 1784 / 105 = 16.99047619

this should have been an integer.

since it's not, round up to 17 to see what happens and round down to 16 to see what happens.

the original equation is 12 * f + 45 * s = 1784.

if s = 17, you get 12 * f + 45 * 17 = 1784.

simplify this to get 12 * f + 765 = 1784.

subtract 765 from both sides to get 12 * f = 1019

solve for f to get f = 1019 / 12 = 84.9...

if s = 16, you get 12 * f + 45 * 16 = 1784

simplify to get 12 * f + 720 = 1784

subtract 720 from both sides to get 12 * f = 1064

solve for f to get f = 1064 / 12 = 88.6

it's still not an integer.

the problem does not look it can be solved for an integer number of flashlights or sleeping bags.

if the total cost is 1785, then you get an integer number of 17 for the number of sleeping bags.

17 * 45 = 765

subtract 765 from 1785 to get 1020

divide 1020 by 12 to get 85

you would get 17 sleeping bags and 85 flashlights.

you said the number of flashlights is 5 times the number of sleeping bags.

17 * 5 = 85

you get a good answer is the total price is 1785 rather than 1784.

hopefully you made a typo and the total price is 1785 rather than 1784.

if the number is 1784 rather than 1785 than you can't get an integer answer.

i would assume 1785 is the correct total amount.

this gives you 17 sleeping bags and 85 flashlights.

Answer by josgarithmetic(39629) (Show Source): You can put this solution on YOUR website!
L, flashlights
b, sleeping bags

System of equations according to the description:

The cost equation after the simple substitution is
and then

b is nearly but not completely whole value. Recheck the description's given information.

Otherwise, 17 sleeping bags and 85 flashlights
(nearest whole numbers)
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