If the ratio of $0.25:x$ is equivalent to $3.25:26$, what is the value of $x$?

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We can convert the ratio notation into a proportion.

$$\frac{0.25}{x}=\frac{3.25}{26}$$

Cross multiply and solve for $x$:

$$0.25\cdot 26 = 3.25 \cdot x$$

We can solve this without using a calculator if we convert the decimals to fractions

$$\frac{1}{4}\cdot 26 = 3 \frac{1}{4} \cdot x$$ $$\frac{1}{4}\cdot 26 = \frac{13}{4} \cdot x$$

Multiplying both sides by 4 allows us to get rid of the fractions on both sides.

$$26 = 13\cdot x$$ $$x=\boxed{2}$$

We can test the answer choices. By inspection, $x$ must be significantly larger than $0.25$ since $26$ is larger than $3.25$. Testing $\boxed{2}$ verifies the solution.

$$\frac{0.25}{x}=\frac{3.25}{26}$$ $$\frac{0.25}{2}=\frac{3.25}{26}$$ $$\frac{1}{4}\cdot \frac{1}{2} =3\frac{1}{4}\cdot \frac{1}{26}$$ $$\frac{1}{8}=\frac{13}{4}\cdot \frac{1}{26}$$ $$\frac{1}{8}=\frac{1}{8}   \checkmark$$