Answer:
1) m=15 and r =5
2) 4 and 2 ml
3) x= 0.5 and y = -1
Step-by-step explanation:
given that m multiple choice questions and r extended response questions.
Also given that a) m+r = total no of questions =20 ... i and
2m+6r = total time taken = 60 ... ii
b) Divide second equation by 2, m+3r = 30 ... iii
m+r = 20 ... i
Subtract to get 2r =10 or r =5
m = 20-5 = 15
Verify: m+r = 15+5 =20
and 2m+6r = 30+30 = 60 minutes.
Hence verified
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2) Let a litres of 20% solution and b litres of 50% solution be mixed
a) Then total volume = 6 ml = a+b ... i
Resulting solution = 30% of 6 ml = 1.8 = 0.2a+0.5b ... ii
b) Solve i and ii
b = 6-a: substitute in ii.
0.2a + 3-0.5a = 1.8
Or a = 4 ml and b = 2ml
Verify: Total volume = a+b =6ml and
concentration = 0.2(4)+0.5(2) = 1.8 = 30% of 6 ml.
Thus verified
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3) 2x-3y=4 ...i
2x-5y =6... ii
Because x term has the same coefficient in both the equations, elimination is easier.
i-ii gives 2y =-2 or y =-1
Substitute in i, 2x+3 =4 or x = 0.5
So answer is x = 0.5 and y =1
