Answer:10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.
Step-by-step explanation:
Let x represent the number of gallons of the 30% solution that should be mixed.
Let y represent the number of gallons of the 70% solution that should be mixed.
The total number of gallons of the mixture to be made is 40. This means that
x + y = 40
The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that
0.3x + 0.7y = 0.6 × 40
0.3x + 0.7y = 24- - - - - - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.3(40 - y) + 0.7y = 24
12 - 0.3y + 0.7y = 24
- 0.3y + 0.7y = 24 - 12
0.4y = 12
y = 12/0.4
y = 30
x = 40 - y = 40 - 30
x = 10
The aides of a right triangle will always satisfy the Pythagorean relationship ...
a² + b²= c²
We can take each of these and try it out:
(1) ... 10² + 24² = 100 + 576 = 676
√676 = <em>26 Yes</em>.
(2) ... 12² + 18² = 144 + 324 = 468
√468 = 21.6, not 20. <em>No.</em>
(3) ... 15² + 26² = 225 + 676 = 901
√901 = 30.017 Awfully close. As an engineer, I'll buy this one. <em>Yes.</em>
(4) ... 40² + 50² = 1,600 + 2,500 = 4,100
√4,100 = 64.03, not 80.<em> No.</em>
-36+(-14)+81=81-36-14=45-14=31
"Non nobis, Domine, non nobis, sed Nomini tuo da gloriam."
Regards M.Y.
