Find the missing number: "Kristen wrote numbers in 5 of the 10 circles..."

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Mathneed

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Kristen wrote numbers in 5 of the 10 circles as shown in the figure.She wants to write a number in each of the remaining 5 circles such that the sums of the 3 numbers along each side of the pentagons are equal. Which number will she have to write in the circle marked by X?


Capture.PNG

Answer options:

a) 7
b)8
c)11
d)13
e)15
 
Mathneed said:
Kristen wrote numbers in 5 of the 10 circles as shown in the figure.She wants to write a number in each of the remaining 5 circles such that the sums of the 3 numbers along each side of the pentagons are equal. Which number will she have to write in the circle marked by X?


View attachment 10659

Answer options:

a) 7
b)8
c)11
d)13
e)15
Click to expand...
Hi, welcome to the forum. We are a math help forum where we help students figure out solution. We do not solve problems for students. If you were to tell us what you tried or where you are stuck I am sure that you will receive expert help. Thank you!
 
I can make a case for all of the listed answers. Is this the whole problem statement? Are there any restrictions on the numbers she can put in the blanks?

-Dan
 
topsquark said:
I can make a case for all of the listed answers. Is this the whole problem statement? Are there any restrictions on the numbers she can put in the blanks?
-Dan
Click to expand...
You sure Dan? I ran scenario where 1 to 99 is the range,
and I get loads of solutions but only 1 solution for x: 13.
 
Denis said:
You sure Dan? I ran scenario where 1 to 99 is the range,
and I get loads of solutions but only 1 solution for x: 13.
Click to expand...

I initially thought we'd need to know what kind of numbers are allowed, and whether they can repeat, but when I actually tried it, I found the same thing you did. I just put a variable in the leftmost space and worked my way around writing expressions, finding that two circles are forced to fixed values, one of them being X.
 
I worked out the answer using basic algebra, but why on earth would anyone think that this is a useful problem for teaching arithmetic?
 
JeffM said:
… why on earth would anyone think that this is a useful problem for teaching arithmetic?
Click to expand...
It could be an assessment of some sort that's secondary to getting a particular answer. We don't have any context, however, so who knows. (Sometimes, teachers aren't teaching per se but simply curious to see what happens! Sometimes, members don't know multiple boards are available.) :cool:
 
Last edited:
Denis said:
… solution for x: 13
Click to expand...
You didn't waste much time, posting the solution so soon. Is that a violation for which one is supposed to spend significant time contemplating in the corner? :p
 
Last edited:
Sorry,

I did not know how to solve the question while posting it, now I got the hint from the reply and solved by using variables to form the equation.

7+3+a=a+1+b
b = 9

x+2+c=15+c
2+x=15
x=13

so d=1 and c= 6.

Answer : x=13.

Thank you.
 
Mathneed said:
Sorry,

I did not know how to solve the question while posting it, now I got the hint from the reply and solved by using variables to form the equation.

7+3+a=a+1+b
b = 9

x+2+c=15+c
2+x=15
x=13

so d=1 and c= 6.

Answer : x=13.

Thank you.
Click to expand...

I take it, then, that although you posted under Arithmetic, an algebraic solution is acceptable?

Good work. That's a little different in detail from what I did, but quite nice.

However, I'm not sure why you say "d=1 and c= 6". We can't tell the value of what you called c in the equation; it could be anything. In fact, whatever a is, c is 5 less than that, and what I imagine you are calling d is 10 less than a. Your values follow if you take a to be 11. (This is why they asked for x, not for a, c, or d.)
 
Thank you.

Got it. Could I know how you solved the problem. Just want to learn from you.
Thank you again.
 
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