Thread: Setting up problem.

I think I did problem #2 right, but I'm confused about problem #1.
I find word problems confusing!!!

#1 The sponsors of a Boys and Girls Club took some members to a play and bought seven more tickets for members than for adults. The members' tickets cost $1.25 and the adults' tickets cost $2.75. If a total of $28.75 was paid for all the tickets, how many members went to the play?


#2 The total receipts for a college basketball game were $674, with a student ticket selling for $1.25 and a non-students ticket selling for 2.75. If there were 136 more students then non-students in attendance, how many people were at the game?


2.75 + 1.25(n+136)=674

2.75 + 1.25+170=674

172.75 + 1.25n=674

1.25n=501.25
n=401

There were 401 people at the game???

Originally Posted by Ash

I think I did problem #2 right, but I'm confused about problem #1.
I find word problems confusing!!!

#1 The sponsors of a Boys and Girls Club took some members to a play and bought seven more tickets for members than for adults. The members' tickets cost $1.25 and the adults' tickets cost $2.75. If a total of $28.75 was paid for all the tickets, how many members went to the play?


#2 The total receipts for a college basketball game were $674, with a student ticket selling for $1.25 and a non-students ticket selling for 2.75. If there were 136 more students then non-students in attendance, how many people were at the game?


2.75 + 1.25(n+136)=674

2.75 + 1.25+170=674

172.75 + 1.25n=674

1.25n=501.25
n=401

There were 401 people at the game???

#2 The total receipts for a college basketball game were $674, with a student ticket selling for $1.25 and a non-students ticket selling for 2.75. If there were 136 more students then non-students in attendance, how many people were at the game?

Umm, let us see.

2.75 + 1.25(n+136)=674
On that first term alone, the "275", you mean there is only 1 non-student in the game? Wrong, isn't it?
That's okay, you're not good at it yet. You'd learn.

Here is one way to do #2.

What does the Problem asks us to find? The number of people at the game.
Who are these people? Students and non-students.

We don't know how many are each, so
let x = number of students
and y = number of non-students.

"If there were 136 more students then non-students in attendance"
So, x = y +136.
Call that Eq. (1).

"... with a student ticket selling for $1.25 and a non-students ticket selling for 2.75"
So, if a student bought a ticket, that student paid $1.25. Hence, since there are x number of students at the game, then all these students paid x*1.25 = 1.25x dollars.
Likewise, the y number of non-students paid y*2.75 = 2.75y dollars.

"The total receipts for a college basketball game were $674,..."
That means
1.25x +2.75y = 674
Call that Eq.(2)

So we have 2 equations with two unknowns:
x = y +136 --------------(1)
1.25x +2.75y = 674 ------(2)

It's easy now, eh?
Let me continue, anyway.

Substitute the value of x in (1) into (2),
1.25(y +136) +2.75y = 674
1.25y +170 +2.75y = 674
1.25y +2.75y = 674 -170
4y = 504
y = 504 /4 = 126 non-students -----**
So, in Eq.(1),
x = y +136
x = 126 +136 = 262 students --------**

Therefore, there are 262 +126 = 388 people at the game. ------answer.

---------
Check,
262(1.25) +126(2.75) =? 674
327.50 +346.50 =? 674
674 =? 674
Yes, so, OK.

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#1 The sponsors of a Boys and Girls Club took some members to a play and bought seven more tickets for members than for adults. The members' tickets cost $1.25 and the adults' tickets cost $2.75. If a total of $28.75 was paid for all the tickets, how many members went to the play?

Find: number of members who went to play.

Who played? Members and adults ( adults are non-members, I understand).
So, let x = number of members who played.

Umm, this Problem #1 is similar to the Problem #2 above. So just follow the procedure there.

Let y = number of adults who played.

As for the total of number of tickets bought,
x = y +7 ---------------(3)

As for the total cost of all the tickets bought,
1.25x +2.75y = 28.75 --------(4)

Since we want to find only the x actually, then we we find the y from (3), or we express the the y in terms of x, in Eq.(3),
y = x -7
Substitute that into 4),
1.25x +2.75(x -7) = 28.75
1.25x +2.75x -19.25 = 28.75
1.25x +2.75x = 28.75 +19.25
4x = 48
x = 48/4 = 12 members

Therefore, 12 members went to play. ------answer.

---------------------
Check,
y = x -7 = 12 -7 = 5 non-members.

12(1.25) +5(2.75) =? 28.75
28.75 =? 28.75
Yes, so, OK.

================================
Word problems are relatively easy to solve if you can interpret them correctly. Be patient and be "exact" with them. Then, check your answers against the meaning of the Problem, to be sure your answers are correct.

Thank you, for taking your time and explaining it very clearly!!!
I understand a lot better now in how to set them up....They're still not my favorite thing to do, but hopefully with more practice they'll become a breeze.