? how to solve

4:5=6:x ?

\(\begin{array}{rcll} 4:5 &=& 6:x \qquad \text{or}\\ \frac45 &=& \frac6x \qquad \updownarrow\\ \frac54 &=& \frac{x}6 \qquad | \qquad \cdot 6\\ 6\cdot \frac54 &=& x \\ x &=& 6\cdot \frac54 \\ x &=& 3\cdot \frac52 \\ x &=& \frac{15}2 \\ \mathbf{x} &\mathbf{=}& \mathbf{7.5} \\ \end{array}\)

4:5=6:x

If 4 goes up to 6, then the ratio is:

6/4=1.5, therefore 5 must go up by the same ratio, so:

5 X 1.5=7.5, so that you have:

4:6=6:7.5