The ratio of the present ages of a mother and her daughter is 7 : 1. Four years ago the ratio of their ages was 19 : 1. What will be the mother's age four years from now ?

Let the present age of the mother be \( 7x \) years and the present age of the daughter be \( x \) years, based on the ratio of their present ages, which is \( 7 : 1 \).

### Step 1: Set up an equation for the ages 4 years ago
Four years ago, the mother's age was \( 7x - 4 \) years and the daughter's age was \( x - 4 \) years. According to the problem, the ratio of their ages at that time was \( 19 : 1 \). Hence, we can write the equation:
\[
\frac{7x - 4}{x - 4} = 19
\]

### Step 2: Solve the equation
Now solve this equation step by step.

\[
7x - 4 = 19(x - 4)
\]
Expand the right side:
\[
7x - 4 = 19x - 76
\]
Move all terms involving \( x \) to one side:
\[
7x - 19x = -76 + 4
\]
\[
-12x = -72
\]
Divide both sides by -12:
\[
x = 6
\]

### Step 3: Find the current ages
Now that we know \( x = 6 \):
- The present age of the mother is \( 7x = 7 \times 6 = 42 \) years.
- The present age of the daughter is \( x = 6 \) years.

### Step 4: Determine the mother's age 4 years from now
Four years from now, the mother's age will be:
\[
42 + 4 = 46 \, \text{years}.
\]

Thus, the mother's age four years from now will be **46 years**.

Would you like more details on the steps or any clarification?

Here are 5 related questions for further practice:
1. What was the daughter's age four years ago?
2. What will the daughter's age be four years from now?
3. If the ratio of their ages changes to 5:1 in 10 years, what will be the mother's age at that time?
4. How many years ago was the ratio of their ages 10:1?
5. If the mother's age were 50 years now, what would the daughter's current age be?

**Tip:** When solving ratio problems, setting up equations from the given ratios is a powerful method to solve for unknowns.

The ratio of the present ages of a mother and her daughter is 7:1. Four years ago, the ratio of their ages was 19:1. What will be the mother's age four years from now?

Solve this algebraic age problem where the ratio of a mother's and daughter's present ages is 7:1, and four years ago it was 19:1. Learn how to set up equations and find the mother's age four years from now. Suitable for Grades 6-8.

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