Determine x/y from the given rational equation.

01 / Standard#Your turn

\frac{3x+5y}{2y-x}=5

Official paper · jm01-2026 · I.2 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Multiply by the nonzero denominator.

Hint 2

Collect the x terms on one side.

Worked solution

The original equation requires a nonzero denominator.
$2y-x\ne0,\quad3x+5y=10y-5x$
If y were zero, x would also be zero, contradicting the denominator condition.
$8x=5y\implies \frac xy=\frac58$

B: 5/8.

Checks and common pitfalls: Do not invert x/y when rearranging the ratio.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The original equation requires a nonzero denominator.
$2y-x\ne0,\quad3x+5y=10y-5x$
If y were zero, x would also be zero, contradicting the denominator condition.
$8x=5y\implies \frac xy=\frac58$

Think first. Reveal a hint when the class is ready.

2026 JM01