Is this a valid math equation?

Question

SH + JU + CH + TO = 120 years old

If SH is 3 years younger than JU and JU is 4 years younger than CH but CH is 1 year older than TO. How old are each of the boys?

**if yes, what is the answer?**

Answer 1

Looks ok to me. It's a little hard to read tho, because you're using two letters for each quantity when only one is customary and only one is necessary.
As for whether or not there is sufficient information to solve this equation uniquely, that's another question. Just eyeballing it, I'd say there is enough information, let me break it down...
SH = JU - 3
JU = CH - 4
CH = TO + 1
Another technicality here ... you are using these letter combinations in two different ways. As names of people, and also as variables for people's ages. So we're abusing the notation a bit. I'll let this slide, tho, and figure the solution. We have four variables and four equations so a solution should be possible. Plugging everything in...
JU - 3 + JU + TO + 1 + TO = 120
2JU - 2 + 2TO = 120
2(CH-4) - 2 +2TO = 120
2CH - 8 - 2 + 2TO = 120
2(TO + 1) - 10 + 2TO = 120
2TO + 2 - 10 + 2TO = 120
4TO - 8 = 120
4TO = 128
TO = 128 / 4 = 32
CH = TO + 1 = 33
JU = CH - 4 = 29
SH = JU - 3 = 26
They're not exatly boys, in their 20's and 30's, but from the first equation it is clear that their average age is 30.
Check: 32 + 33 + 29 + 26 = 120

Answer 2

Let x = the age of TO
then the age of CH = x + 1
the age of JU = CH - 4 = (x+1) -4 = x-3
the age of SH = JU - 3 = (x-3) -3 = x-6, now add them
SH+JU+CH+TO = (x-6) + (x-3) + (x+1) + x
= 4x + (-6-3+1) = 4x - 8 = 120
4x = 120 + 8 = 128
x = 128/4 = 32 = age of TO and the rest is easy

Answer 3

Yes, the following is a valid statement.

CH is 1 year older than TO who is 3 years older than JU who is 3 years old than SH.

CH= 33
TO= 32
JU= 29
SH= 26

120/4= 30
Easiest way is to guess a number in the 30's and work from there.

Answer 4

SH + JU + CH + TO = 120 ... ... (1)
SH + 3 = JU
JU + 4 = CH
CH - 1 = TO

TO = CH - 1 = JU + 4 -1 = SH + 3 + 4 - 1 = SH + 6
CH = JU + 4 = SH + 3 + 4 = SH + 7
JU = SH + 3

Substituting in equation (1)
SH +(SH +3) + (SH + 7) +(SH + 6) = 120
4 SH + 16 = 120
4 SH = 120 - 16 = 104
SH = 104 / 4 = 26


SH = 26 years
JU = SH + 3 = 29 years
CH = SH + 7 = 33 years
TO = SH + 6 = 26 + 6 = 32 years

Answer 5

S + J + C + T = 120

(I'm going to use a single letter to represent everybody to avoid confusion).

S is 3 years younger than JU ----> S = J - 3
J is 4 years younger than C ----> J = C - 4
C is 1 year older than T ------> C = T + 1

Seeing as we're given S + J + C + T = 120, let's do the substitution one at a time.

S + J + C + T = 120

S = J - 3, so

(J - 3) + J + C + T = 120. Simplifying, we get
2J + C + T = 123

J = C - 4, so

2(C - 4) + C + T = 123
2C - 8 + C + T = 123
C + T = 131

C = T + 1, so

(T + 1) + T = 131
2T + 1 = 131
2T = 132, therefore,
T = 66

Now that we know T is 66 years old, we can derive the others. Remember that
S = J - 3
J = C - 4
C = T + 1

C = 66 + 1 = 67
J = C - 4 = 67 - 4 = 63
S = J - 3 = 63 - 3 = 60

Therefore, C is 67, J is 63, S is 60, and T is 66.

Answer 6

Yeah, but that's not how you solve it. It's only part of it.

1. SH = JU - 3
2. JU = CH - 4
3. CH = TO + 1

You want to get everything in terms of one variable.. I say JU

SH = JU - 3

JU = JU

JU = CH - 4
JU + 4 = CH
CH = JU + 4

CH = TO + 1
JU + 4 = TO + 1
JU + 3 = TO
TO = JU + 3

Now we have 4 equations, all in terms of JU:

SH = JU - 3
JU = JU
CH = JU + 4
TO = JU + 3

Now put this in your original equation

SH + JU + CH + TO = 120
JU - 3 + JU + JU + 4 + JU + 3 = 120
4JU + 4 = 120
4(JU + 1) = 120
JU + 1 = 30
JU = 29

JU is 29. Now plug these in your 4 equations to find the other ppl.

SH = JU - 3 = 29 - 3 = 26
JU = 29
CH = JU + 4 = 29 + 4 = 33
TO = JU + 3 = 29 + 3 = 32

Answer 7

if age of TO = x
then age of CH = x+1
age of JU = x+1-4 = x-3
age of SH = x-3-3= x-6
therefore x + (x+1) + (x-3)+ (x-6) = 120
4x - 8 = 120
4x = 128
x = 32
TO = 32
CH = 33
JU = 29
SH = 26

Answer 8

SH = TO + 1 - 4 -3 = 26
JU = TO + 1 - 4 = 29
CH = TO + 1 = 33
TO = 32

120 = 4TO + 8
TO = (120 + 8): 4
TO = 32 y.o.
Answer: 26, 29, 33, 32y.o, respectively.
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Answer 9

So far...

Now set up the other equations, for example:

SH + 3 = JU etc...