Question

Pam is playing with red and black marbles. The number of red marbles she has is three more than twice the number of black marbles she has. She has 42 marbles in all. How many red marbles does Pam have?

Answer 1

three more than twice the number of black
3 + 2b

so r= 3+2b
also b+r= 42
can you finish ?

Answer 2

the number of red marbles (R) is three more than twice the black (B)
R = 2B + 3

42 marbles in all
R + B = 42

substitute 2B + 3 for R into the second equation
2B + 3 + B = 3B + 3 = 42

subtract 3 from both sides
3B = 39

divide by 3 on both sides
B = 13

substitute 13 for B in second equation
R + B = R + 13 = 42

subtract 13 from both sides
R = 29

so pam has 29 red and 13 black marbles

Answer 3

three more than --> 3+
twice number of black --> 2 b

Answer 4

ok so r=2b+3

Answer 5

sorry seiga it kind of confused me... when you wrote 2b+3+b=3b+3=42 where did you get the 3b+3 from?

Answer 6

r= 2b+3
r+b= 42

we can solve these using substitution or elimination. I'll show elimination
re-write r= 2b+3 as r - 2b = 3 (add -2b to both sides)
we now have

r - 2b = 3
r + b= 42

multiply the bottom equation by -1 (that means both sides , all terms)

r - 2b = 3
-r - b = -42

now add the equations together. what do we get ?

Answer 7

can you show subsstitution? sorry

Answer 8

See http://www.khanacademy.org/math/trigonometry/systems_eq_ineq/systems_tutorial_precalc/v/simple-elimination-practice
for a quick example

Answer 9

if you want to use substitution:

we have r= 2b+3
and r+b= 42
replace r with 2b+3 in the 2nd equation
2b+3+b = 42
can you finish ?

Answer 10

yes

Answer 11

i did it thanks