Question

The Smith family consists of four people. Anna is three years older than Matthias. Ms. Smith is four times as old as Anna. Mr. Smith is five years older than his wife. Together they are 72 years. How old are the family members?

A) Anna is 7, Matthias is 4, Ms. Smith is 28, and Mr. Smith is 33.
B) Anna is 4, Matthias is 7, Ms. Smith is 33, and Mr. Smith is 28.
C) Anna is 12, Matthias is 9, Ms. Smith is 45, and Mr. Smith is 50.
D) Anna is 6, Matthias is 3, Ms. Smith is 24, and Mr. Smith is 29.

Answer 1

By creating equations from the information given, we deduced Anna's age first and used it to calculate the ages of Matthias, Ms. Smith, and Mr. Smith. The correct ages of the Smith family members are Anna 7, Matthias 4, Ms. Smith 28, and Mr. Smith 33.

Step-by-step explanation:

To solve the problem, we need to use the information given to create equations and solve for the members of the Smith family.

• Let's denote Anna's age as A.
• Matthias's age will then be A - 3 (since Anna is three years older than Matthias).
• Ms. Smith's age is 4A (since she is four times as old as Anna).
• Mr. Smith's age is 4A + 5 (since he is five years older than Ms. Smith).

Adding up all their ages should give us the total of 72 years:

A + (A - 3) + 4A + (4A + 5) = 72

Simplifying the equation, we get:

10A + 2 = 72

Subtract 2 from both sides to get:

10A = 70

Divide both sides by 10 to find Anna's age:

A = 7

Now we can calculate the age of each family member:

• Anna is 7 years old.
• Matthias is 7 - 3 = 4 years old.
• Ms. Smith is 4 * 7 = 28 years old.
• Mr. Smith is 28 + 5 = 33 years old.

Therefore, the correct answer is:

A) Anna is 7, Matthias is 4, Ms. Smith is 28, and Mr. Smith is 33.