Let X represent Karma's fathers age and Y represent Karma's age. The first term can be found using this formula:
Y = 1/3X → 5 Years ago
Y = 1/2X → 5 Years from now
From mental math, I can concur she's 15 and her father is 35. Then we plug in to check.
1/3(30) = 10 √ (Five years ago).
1/2(40) = 20 √ (Five years from current).
Their current ages are 15 and 35.
Let t and s represent the masses of 20% and 60% alloys respectively.
t+s=80, s=80-t
(0.2t+0.6s)/80=0.52 multiply both sides by 80
0.2t+0.6s=41.6, now using s=80-t in this equation gives us:
0.2t+0.6(80-t)=41.6 perform indicated multiplication on left side
0.2t+48-0.6t=41.6 combine like terms on left side
-0.4t+48=41.6 subtract 48 from both sides
-0.4t=-6.4 divide both sides by -0.4
t=16, since s=80-t
s=64
So 16kg of 20% alloy is mixed with 64kg of 60% allow to make 80kg of a 52% alloy.
An 311
Step-by-step explanation:
Mean:12
median:11.5
mode:16
range:10