Question

A baby is 20 1/2 inches long at birth. The baby grows at a rate of 1 1/12 inches per month. At the end of how many months will the baby be 27 inches long?

Answer 1

The baby will be 27 inches long at the end of approximately 6 months.

Step-by-step explanation:

To solve this problem, we can set up an equation. Let x represent the number of months it takes for the baby to reach a length of 27 inches.

The initial length of the baby is 20 1/2 inches. From there, the baby grows at a rate of 1 1/12 inches per month. So, the length of the baby after x months can be represented as 20 1/2 + (1 1/12)x.

We need to find the value of x when the length of the baby is 27 inches. So, we can set up the equation 20 1/2 + (1 1/12)x = 27 and solve for x.

Subtracting 20 1/2 from both sides of the equation gives us (1 1/12)x = 27 - 20 1/2.

Simplifying the right side of the equation gives us (1 1/12)x = 6 1/2.

To solve for x, we can convert the fractions to decimals. (1 1/12) is equivalent to 1.0833.

So, the equation becomes 1.0833x = 6.5.

Dividing both sides of the equation by 1.0833 gives us x = 6.5 ÷ 1.0833 ≈ 6.

Therefore, the baby will be 27 inches long at the end of approximately 6 months.

Answer 2

To find out after how many months a baby that is 20 1/2 inches at birth will reach 27 inches, given a growth rate of 1 1/12 inches per month, calculate the total growth required and divide by the monthly rate. The baby will reach 27 inches long after 6 months.

Step-by-step explanation:

The question deals with the growth of a baby in terms of length. In this case, the baby is 20 1/2 inches long at birth and grows at a constant rate of 1 1/12 inches per month. To find out how many months it will take for the baby to reach 27 inches long, we need to determine the total growth needed to reach 27 inches from 20 1/2 inches and then divide it by the monthly growth rate.

• First, calculate the total growth needed: 27 inches - 20 1/2 inches = 6 1/2 inches.
• Next, convert the mixed numbers to improper fractions for easier calculation. So, 20 1/2 becomes 41/2 and 1 1/12 becomes 13/12. Now subtract to find: 27 inches - 41/2 inches = 54/2 - 41/2 = 13/2 inches (or 6 1/2 inches).
• To find the number of months, divide the total growth needed by the monthly growth rate: 13/2 inches divided by 13/12 inches/month yields the number of months.
• The calculation will be (13/2) ÷ (13/12) = (13 × 12) / (2 × 13) = 156/26 = 6.

Therefore, the baby will be 27 inches long at the end of 6 months.