the ratio of a mothers age to her daughters is 5:2. in 10 years, the ratio will be 7:4. how old is mother…
the ratio of a mothers age to her daughters is 5:2. in 10 years, the ratio will be 7:4. how old is mother now?\n25\n20\n35\n22\n10
Answer
Explanation:
Step1: Let the mother's current age be $5x$ and daughter's be $2x$.
Set up the age - ratio equation for 10 years later.
Step2: In 10 years, mother's age will be $5x + 10$ and daughter's will be $2x+10$. The ratio equation is $\frac{5x + 10}{2x + 10}=\frac{7}{4}$.
Cross - multiply: $4(5x + 10)=7(2x + 10)$.
Step3: Expand both sides.
$20x+40 = 14x + 70$.
Step4: Move the $x$ terms to one side and constants to the other.
$20x-14x=70 - 40$. $6x=30$.
Step5: Solve for $x$.
$x = 5$.
Step6: Find the mother's current age.
Mother's current age is $5x$, so $5\times5 = 25$.
Answer:
A. 25