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ext{ $2$ years ago } \frac{ $1$ }{ $4$ } ext{ of Udin's age } = \frac{ $2$ }{ $3$ } ext{ of Asep's age, if next year Udin's age is } $3$ x ext{ Asep's age, how old are Udin and Asep now.}

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Add and subtract rational numbers: word problems

Full solution

Q. ext{

2

years ago } \frac{

1

}{

4

} ext{ of Udin's age } = \frac{

2

}{

3

} ext{ of Asep's age, if next year Udin's age is }

3

x ext{ Asep's age, how old are Udin and Asep now.}

Set Up Equations: Let's call Udin's age $2$ years ago $U$ and Asep's age $2$ years ago $A$ . The first equation from the problem is $\frac{1}{4} U = \frac{2}{3} A$ .
Express Current Ages: Now, let's express Udin's current age as $U + 2$ and Asep's current age as $A + 2$ .
Formulate Second Equation: Next year, Udin's age will be $U + 3$ and Asep's age will be $A + 3$ . The second equation from the problem is $U + 3 = 3 \times (A + 3)$ .
Solve for U: Let's solve the first equation for U. Multiply both sides by $4$ to get rid of the fraction: $U = \left(\frac{2}{3} \times A\right) \times 4$ .
Substitute $U$ in Equation: Simplify the equation: $U = \frac{8}{3} \times A$ .
Distribute and Simplify: Now, substitute $U$ in the second equation with $\frac{8}{3} \times A$ : $\frac{8}{3} \times A + 3 = 3 \times (A + 3)$ .
Finalize Solution: Distribute the $3$ on the right side of the equation: $\frac{8}{3} \times A + 3 = 3A + 9$ .
Finalize Solution: Distribute the $3$ on the right side of the equation: $\frac{8}{3} * A + 3 = 3A + 9$ .To solve for $A$ , first multiply every term by $3$ to get rid of the fraction: $8A + 9 = 9A + 27$ .

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