I think this is algebra...?

Question

Alyssa is 12 years younger than Michelle. Michelle is 7 years older than twice Amanda's age The sum of all three ages is 47. How old is Michelle?

Please help me

Answer 1

Setup:

Amanda's age= x

Michelle is 7 years older than twice Amanda's age, so Michelle is (2x + 7).

Alyssa is 12 years younger than Michelle, so Alyssa is (2x + 7) - 12 = 2x - 5.

Step 1: The sum of all three ages is 47, so we have the equation: [x + (2x + 7) + (2x - 5) = 47]

Step 2: 5x + 2 = 4, we will subtract 2 from each side because whatever we do to one side we do to the other. This will result in 5x = 45, we can divide 5 from both sides to get x = 9

Step 3: Michelle's age is (2x + 7), so plug in (x = 9): [2(9) + 7 = 18 + 7 = 25]

Answer: Michelle is 25​ years old.

Answer 2

First, the problem says Alyssa is 12 years younger than Michelle. That means if we call Michelle’s age M, then Alyssa’s age is M minus 12.

Next, Michelle is 7 years older than twice Amanda’s age. If Amanda’s age is A, then twice Amanda’s age is 2A, and Michelle’s age is 2A plus 7. So, we now have two expressions for Michelle’s age:

1. From Alyssa’s side, Michelle is M
2. From Amanda’s side, Michelle is 2A + 7

Since both represent Michelle’s age, they must be equal. So:

M = 2A + 7

We also know Alyssa’s age is M - 12.

The problem says the sum of all three ages is 47, so:

A + M + (M - 12) = 47

Substitute M = 2A + 7 into this equation:

A + (2A + 7) + (2A + 7 - 12) = 47

Simplify it:

A + 2A + 7 + 2A - 5 = 47

(A + 2A + 2A) + (7 - 5) = 47

5A + 2 = 47

Subtract 2 from both sides:

5A = 45

Divide by 5:

A = 9

Now that we know Amanda is 9, find Michelle’s age:

M = 2A + 7 = 2×9 + 7 = 18 + 7 = 25

So, Michelle is 25 years old.

Answer 3

Let x = Michelle's age

y = Amanda's age

z= Alyssa's age

z = x - 12 (Alyssa is 12 years younger than Michelle)

x = 2y + 7 (Michelle is 7 years older than twice Amanda's age)

From that last equation: 2y = x - 7, y = (1/2)(x-7)

At this point we have all three ages in terms of x (Michelle's age).

x = Michelle's age

y = (1/2)(x - 7)

z = x - 12

If you add all 3 ages together you get 47:

x + (1/2)(x - 7) + (x - 12) = 47

At this point one technique for solving the equation is to multiply every term by 2 to clear the fraction:

2x + (x - 7) + 2(x - 12) = 94

2x + x - 7 + 2x - 24 = 94

5x - 31 = 94

5x = 125

x = 25 (Michelle)

y = (1/2) (25 - 7) = 9 (Amanda)

z = 25 - 12 = 13 (Alyssa)

Answer 4

Let x = Amanda's age

Then, 2x + 7 = Michelle's age and (2x + 7) - 12 = Alyssa's age

So, x + (2x + 7) + [(2x + 7)- 12] = 47

5x + 2 = 47

5x = 45

x = 9

Amanda is 9 years old, Michelle is 25 years old, and Alyssa is 13 years old.

Answer 5

Let:

A = Alyssa’s age = (B -12)

B = Michelle’s age = (2C + 7)

C = Amanda’s age = ((B - 7)/2)

B + (B - 12) + ((B - 7)/2) = 47

Combine like terms:

2B + B/2 - 12 - 7/2 = 47

Place unknown (B) on left side of equation and move constants to the by inverse operation.

5B/2 = 94/2 + 31/2

Multiply every term by 2 and then combine the constants on right side of equation.

5B = 125

B = 25 years old = Michelle’s current age.

Check answer:

(25-12) + 25 + ((25 - 7)/2) =

13 + 25 + 9 = 47

Checks out.

Answer 6

Answer 7

Let's define the variables:

1. Let Amanda's age = A
2. Michelle is 7 years older than twice Amanda's age:
3. → Michelle's age = 2A + 7
4. Alyssa is 12 years younger than Michelle:
5. → Alyssa's age = (2A + 7) - 12 = 2A - 5

Now, the sum of all their ages is 47:

A+(2A+7)+(2A−5)=47

Simplify:

A+2A+7+2A−5=47

5A+2=47

5A=45

A=9

Now find Michelle's age:

Michelle=2A+7=2(9)+7=18+7=25

Michelle is 25 years old.

Answer 8

Alyssa is 12 years younger than Michelle. Michelle is 7 years older than twice Amanda's age The sum of all three ages is 47. How old is Michelle?

Michelle = M = 2A + 7 (7 years older than twice Amanda's age)

Alyssa = M - 12

Amanda = A

We want each person's variable to be represented by the same variable. Let's substitute Alyssa's (M) with M = 2A + 7. Now we have :

A + 2A + 7 - 12 + 2A + 7 = 47

combine like terms -----> 5A + 2 = 47

= 5A = 45 so A = 9 years old. Amanda is 9 years old. Michelle is 9(2) + 7 = 25 years old. Alyssa is 25 - 12 = 13 years old.