Need help with a simultaneous equation!?

Question

Solve using simultaneous equations:

Flour is sold in packets of 5kg and 2kg. The 5kg packets cost $2.75 each and the 2kg packets cost $1.25 each. If I bought 67kg of flour and the total cost was $38.50, how many of each kind of packet did I buy?

Full working out would be so appreciated :)

Thank you so much!

Answer 1

Hi,

5x + 2y = 67 (kilograms + kilograms = total kilograms)
2.75x + 1.25y = 38.50 (money for "x" 5 kg bags + money for "y" 2 kg bags = total money)

Multiplying the top equation by 5 and the bottom equation by -8 gives the following equations:

5(5x + 2y = 67)
-8(2.75x + 1.25y = 38.50)

25x + 10y = 335
-22x - 10y = -308

Adding these equations together will cause y to drop out so we can solve for x.

3x = 27
x = 9, so 9 5kg bags were sold. <== answer

Since 5x + 2y = 67 and x = 9, we can solve for y:
5x + 2y = 67
5(9) + 2y = 67
45 + 2x = 67
2x = 22
x = 11, so there were 11 2 kg bags of flour sold. <== answer

I hope that helps!! :-)

Answer 2

Let there are x 5kg packets, and y 2kg packets.
Equation :
5x + 2y = 67 ... (1)
2.75x + 1.25 y = 38.5 ... (2)
8 * (2) --> 22x + 10y = 308 ...(2)'
5 * (1) --> 25x + 10y = 335 ...(1)'
(1)'-(2)' --> 3x = 27
x = 9
Subsitute x to first equation : 5*9 + 2y = 67
45 + 2y = 67
2y = 22
y = 11
So, you're buying 9 5kg packets and 11 2kg packets.

Answer 3

Let x=5kg. packets.
Let y= 2kg. packets
5x+2y=67
2.75x +1.25y=38.50
From the first equation,
2y=67-5x
y=(67-5x)/2
Substitute this into the second equation
to get 2.75x+1.25(67-5x)/2=38.50
2.75x+(83.75-6.25x)/2=38.50
(2)(2.75x)+83.75-6.25x=2(38.5)
5.5x-6.25x=77-83.75
-0.75x=-6.75
75x=675
x=9
5x+2y=67
5(9)+2y=67
2y=67-45
2y=22
y=11
9-5kg. packets, 11-2kg. packets
Check:
9(2.75) + 11(1.25)
=24.75 + 13.75, =38.50
Our answers are correct.

Answer 4

5x+2y=67
2.75x+1.25y=38.5
275x+125y=3850
275x+110y=3685
15y = 165
y=11
5x+22=67
5x=45
x=9

9 5kg packets and 11 2kg packets