Jean is seven years older than her brother Bob if he is three years older than their sister Mary. If the sum of their ages is 40 Siri how old is each you must set up an equation, solve and explain each step

J = B + 7

B = M + 3 so J = M+3+7

J + B + M = 43

(M+3+7) + (M+3) + M = 43

3 M + 13 = 43

3 M = 30

M = 10
now go back and get Bob and Jean

Sum is 43 not 40 sorry

Let's start by assigning variables to each person's age:

Let's say Bob's age is represented by 'B'.
Given that Bob is three years older than Mary, we can represent Mary's age as 'M'.
Since Jean is seven years older than Bob, we can represent Jean's age as 'J'.

Now, we are given that the sum of their ages is 40. We can set up the following equation:

B + M + J = 40

We also have the additional information that Bob is three years older than Mary:

B = M + 3

And that Jean is seven years older than Bob:

J = B + 7

To solve this system of equations, we can substitute the values of B and J into the first equation:

(M + 3) + M + (M + 3 + 7) = 40

Simplifying this equation, we get:

3M + 13 = 40

Next, we can subtract 13 from both sides of the equation:

3M = 40 - 13
3M = 27

Finally, divide both sides by 3 to isolate M:

M = 27 / 3
M = 9

Now that we have found Mary's age as 9, we can substitute this value back into the equation for B:

B = M + 3
B = 9 + 3
B = 12

Finally, we can substitute the values of M and B back into the equation for J:

J = B + 7
J = 12 + 7
J = 19

Therefore, Mary is 9 years old, Bob is 12 years old, and Jean is 19 years old.

To solve this problem, let's assign variables to the unknown ages. Let's say Jean's age is represented by 'J', Bob's age by 'B', and Mary's age by 'M'.

According to the problem statement, we have the following information:

1. Jean is seven years older than Bob: J = B + 7.

2. Bob is three years older than Mary: B = M + 3.

3. The sum of their ages is 40: J + B + M = 40.

Now, let's solve the system of equations step by step:

Step 1: Substitute the value of B from equation (2) into equation (1):
J = (M + 3) + 7.

Step 2: Simplify equation (1):
J = M + 10.

Step 3: Substitute the values of J (from equation 3) and B (from equation 2) into equation (3):
(M + 10) + (M + 3) + M = 40.

Step 4: Simplify equation (3):
3M + 13 = 40.

Step 5: Subtract 13 from both sides of the equation:
3M = 27.

Step 6: Divide by 3:
M = 9.

Now that we've found the value of M, we can find the ages of Jean and Bob:

Substituting the value of M into equation (2):
B = 9 + 3,
B = 12.

Substituting the value of B into equation (1):
J = 12 + 7,
J = 19.

Therefore, Jean is 19 years old, Bob is 12 years old, and Mary is 9 years old.