I find it easier to start from scratch and write out the equations, then compare them with the given equations.
Let m and j represent the ages of the two boys. Then m-5=(2/3)(j-5)
Also, in ten years: m+10 = (5/6)j.
Let's solve this system: Mult the first eqn by 3 to remove the fraction:
3(m-5) = 2(j-5), or 3m - 15 = 2j -10. Next, mult. the 2nd eqn by 6 to remove the fraction: 6m+60 = 5j.
Our two equations are (at this point) 3 m - 15 = 2j - 10 and
6m +60 = 5j
Let's mult. the first equation by -2, so as to obtain the coefficient -6 for m:
-6m + 30 = -4j + 10
6m + 60 = 5j
---------------------------
90 = j + 10, so j = 80 (wow!)
Let's now find m: 6m + 60 = 5(80), or 6m = 400+60 = 460
Then m = 76 2/3.
We must check our solution (m = 76 2/3, j = 80):
Let's subst. these values into m-5=(2/3)(j-5)
Does 76 2/3 - 5 = (2/3)(80) - 10/3?
Does 76 2/3 - 15/3 = 160/3 - 10/3?
Does 76 - 15 = 160 - 10 No. So something's wrong here.
Going back to the problem statement:
<span>x-5=2/3(y-5) and x+10=5/6(y+10) seems correct!
Mike's age 5 years ago was x-5, and james' age 5 years ago was y-5. The multiplier (2/3) is also correct.
Mikes age 10 years from now will be x+10, and james' y+10.
The first answer set is the correct one.</span>
Answer:
what does the picture say?
Step-by-step explanation:
Let 'x' represent the volume of 6% saline solution
Let 'y' represent the volume of 8% saline solution
Form 2 equations.
Eq. 1: 20+x=y
Meaning 20 cm³ + x cm³=y cm³
Eq 2: 0.06x+0.1(20)=0.08y
Meaning: 6% of x + 10% of 20= 8% of y
Use substitution or elimination to solve this linear system. I used substitution.
Sub. Eq. 1 (20+x=y) into Eq. 2 (0.06x+0.1(20)=0.08y)
0.06x+ 0.1(20)=0.08(20+x)
0.06x+2+1.6=0.08x
-0.02x= -0.4
x=20
Substitute x=20 into equation 1 (you can also use 2 but in this case equation 1 is simpler)
20+x=y
20+20=y
40=y
To check, substitute x=20 and y=40 into equation 2
0.06x + 0.1(20)= 0.08y
0.06(20) +2 = 0.08(40)
1.2+2= 3.2
3.2=3.2
Therefore, Kim would need 20cm³ of 6% saline solution and 40cm³ of 10% saline solution to make 8% solution.
Answer:
x = 0
Step-by-step explanation:
Slope = change in y/change in x
Slope = 5-3/1-x
2 = 2/1-x
2(1 - x) = 2
2 - 2x = 2
2 = 2 - 2x
0 = -2x
x = 0
-Chetan K
