Question

[6.02] Use a system of equations to solve the following problem: Charles High School has a total of 94 boys and girls who play sports. If the number of boys is 22 more than twice the number of girls, how many boys play sports at this high school?

70

48

24

80

Answer 1

No. You may not top post and ignore the answer that was being given to you.

Answer 2

Like I said the last time you posted it, set up two variables
B = number of boys
G = number of girls

What now are two equations you can write down with B and G?

Answer 3

idk

Answer 4

"Charles High School has a total of 94 boys and girls who play sports"
How do you turn that into one equation involving B and G? Any ideas?

Answer 5

94=b+g ??

Answer 6

Yes.

Now, what about a second equation.

Answer 7

"number of boys is 22 more than twice the number of girls"

Answer 8

b+22=g

Answer 9

Not quite. B = G + 22, because the number of boys, B, is more than G.

Answer 10

Hence you have two equations
B + G = 94
B - G = 22

(where I rewrote the second equation, B = G + 22)

So far so good?

Answer 11

oh ok

Answer 12

why is it b-g=22 ??

Answer 13

Do you agree that B = G + 22 ?

Answer 14

If so, then subtract G from each side:
B - G = G + 22 - G
i.e.,
B - G = 22

Answer 15

im confused a little , sorry

Answer 16

Never mind about that then. What are the two equations from your point of view?

Answer 17

94=b+g
B = G + 22

Answer 18

Right.
B + G = 94

B = G + 22

Two linear equations in two unknowns. Now solve them. Do you know how?

Answer 19

we wanna get b by it self so - g on each side right ?

Answer 20

Well, I would substitute the second equation into the first equation.

Answer 21

Substitute
B = G + 22
into
B + G = 94

Answer 22

ok then what do i do my teacher didnt show me how to do thaat ?

Answer 23

i worked it out and got 24 am i right ??

Answer 24

This is the standard way to solve simultaneous equations in high school.

If you do that then we have

B + G = 94

(G + 22) + G = 94

2G + 22 = 94

Now see what to do?

Answer 25

(and btw, 24 is not the value of B or G)

Answer 26

yes then you divide 2 into 94 and 2 right ?

Answer 27

You could divide the entire equation by 2, in which case you would have
2G + 22 = 94
=> G + 11 = 47

Answer 28

yes then u subtract 11 from 47

Answer 29

Hence G = ... what?

Answer 30

36 but thats not a choice tho

Answer 31

For B or G?

If G = 36, what does B have to be?

Answer 32

58?

Answer 33

Yes
B = 58
G = 36

We can verify that is the answer by making sure those values satisfy the equations
B + G = 94
B = G + 22

which indeed they do.

Answer 34

but thats not a choice tho and he 4 answers

Answer 35

No, it's not. So what's wrong? What's wrong is our second equation didn't correspond to the question: "boys is 22 more than twice the number of girls"

Answer 36

Hence the second equation should have been
B = 2G + 22

Answer 37

So instead, solve the system
B + G = 94
B = 2G + 22

Answer 38

ohhh meaning it would of been 48

Answer 39

Really? How'd you get that?

Answer 40

Work through the algebra again, now with the correct equations.

Answer 41

bec ause if u divide 2 into 22 it would be 11 then you add that to the to 37 (hence like we did before cus we added the 22 to 37) IN CONCLUSION IT WOULD ADD TO 48!!!! YAY !!!

Answer 42

Wrong.

Answer 43

B + G = 94
B = 2G + 22

Substitute the second equation into the first equation.

Answer 44

IM CONFUSED UGHH

Answer 45

These are the correct two equations
B + G = 94
B = 2G + 22

You need to solve them. The way to solve them is to use the substation technique we saw above. To do that, substitute the second equation into the first equation and eliminate the variable B:

Answer 46

*substitution

Answer 47

24

Answer 48

What's 24?