Question

Seven times my age, plus three times my mother's age,is 218 years.Nine times my mother's age, minus seven times my

age, is 262 years.
How old is my mother? How old am I?

Answer 1

To solve this problem, we can set up a system of equations using the given information. By using either substitution or elimination, we can find the age of the student's mother. However, the age of the student cannot be determined precisely.

Step-by-step explanation:

To solve this problem, let's assign variables to the ages of the student (S) and the mother (M). We can set up a system of equations based on the given information:

1. 7S + 3M = 218 (Equation 1)
2. 9M - 7S = 262 (Equation 2)

To solve this system, we can use either substitution or elimination.

Using substitution:

1. From Equation 1, we can express S in terms of M: S = (218 - 3M) / 7
2. Substitute this expression for S in Equation 2: 9M - 7((218 - 3M) / 7) = 262
3. Simplify and solve for M: 9M - (218 - 3M) = 262
4. Combine like terms: 12M - 218 = 262
5. Add 218 to both sides: 12M = 480
6. Divide both sides by 12: M = 40

Using elimination:

1. Multiply Equation 1 by 9 and Equation 2 by 7: 63S + 27M = 1962 (Equation 3) and 63M - 49S = 1834 (Equation 4)
2. Add Equations 3 and 4 to eliminate the variable S: (63S - 49S) + (27M + 63M) = 1962 + 1834
3. Simplify and solve for M: 14M = 3796
4. Divide both sides by 14: M = 271

Considering the given information, it seems that the age of the student cannot be determined precisely. However, the age of the student's mother is either 40 (using substitution) or 271 (using elimination).