System of Equations (word problem)?

Question

you are on the prom committee and are in charge of buying balloons. You want to use both latex and mylar balloons. the latex balloons cost $.10 each and the mylar balloons cost $.50 each. you need 125 balloons and you have $32.50 to spend. how many of each can you buy?

Answer 1

75 latex balloons

50 mylar balloons



x=number of latex balloons

y=number of mylar balloons

equation one: x+y=125

y=125-x



equation two:

.10x + .50y=32.5

[.10x + .50(125-x) =32.5] multiply the entire equation by 10 to clear decimals



1x+5(125-x)=325

x+625-5x=325

x-5x= -300



-4x=-300

x=75

y=50

75 latex balloons

50 mylar balloons

Answer 2

so lets say x=the # of latex balloons and y=the # of mylar balloons

you need 125 balloons total so your first equation is x+y=125

you have $32.50 to spend so your second equation is .10x+.50y=32.50 (because each latex ballon, x, costs 10cents and each mylar ballon, y, costs 5o cents.) then solve for x and y.



x+y=125, subtract y from both sides and get x=125-y

then plug that in for x in the second equation:



.10(125-y)+.50y=32.50. then solve for y and thats the number of mylar balloons you can get.



when you have y, you can plug that number in for y in the equation x+y=125 and get x, which is how many latex balloons you can get.

Answer 3

(L)atex + (M)ylar =125

L=125-M



.1(L)+.5(M)=32.5



substitute 125-M for L

.1(125-M)+.5(M)= 32.5



12.5-.1(M)+.5M=32.5

.4(M)=20

M=50



L+M=125

L=75



.1(75)+.5(50)=32.5

7.5+25=32.5

32.5=32.5



You can buy 50 Mylar balloons and 75 Latex

Answer 4

introduce variables x and y, or the like:



(1) .1x + .5y = 32.50

(2) x + y = 125



multiply eq'n 1 by 10, and subtract eq'n 2. Solve for y. Solve for x.





-D Phil