I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
Answer:
x = 3 , y = 1
Step-by-step explanation:
2x + y = 7
3x + y = 8
solution
2x + y = 7-----------(1)
3x - y = 8------------(2)
from equation 1
2x + y = 7
y = 7 - 2x-------------(3)
substitute equation 3 into equation 2
3x - y = 8
3x - (7 - 2x) = 8
3x - 7 + 2x = 8
3x + 2x = 8 + 7
5x = 15
divide through by the coefficient of x
5x/5 = 15/5
x = 3
to find y
substitute x into equation 1
2x + y = 7
2(3) + y = 7
6 + y = 7
y = 7 - 6
y = 1
Answer:
Each book cost $3.55
Step-by-step explanation:
7 guests
It costs 5 dollars per guest, so divide 35 by 5
