Respuesta :
Let's begin by identifying key information given to us:
Let ring be represented as x
Let heart be represented as y
Let hat be represented as z
[tex]\begin{gathered} ring\times heart=hat\Rightarrow x\cdot y=z \\ hat\times2=heart\Rightarrow z\cdot2=y\Rightarrow y=2z \\ heart-ring=\frac{1}{4}\Rightarrow y-x=\frac{1}{4} \\ x\cdot y=z-----1 \\ y=2z------2 \\ y-x=\frac{1}{4}----3 \end{gathered}[/tex]We will calculate for the unknown from the equations:
[tex]\begin{gathered} x\cdot y=z------1 \\ y=2z-------2 \\ y-x=\frac{1}{4}-----3 \\ \text{Substitute equation 2 into }equation\text{ 1:} \\ x(2z)=z \\ \text{Divide both sides by ''z'', we have:} \\ \frac{x(2z)}{z}=\frac{z}{z}\Rightarrow2x=1 \\ 2x=1 \\ x=\frac{1}{2} \\ \text{Substitute the value of ''x'' into equation 3, we have:} \\ y-x=\frac{1}{4}\Rightarrow y-\frac{1}{2}=\frac{1}{4} \\ y-\frac{1}{2}=\frac{1}{4} \\ y=\frac{1}{4}+\frac{1}{2}=\frac{3}{4} \\ y=\frac{3}{4} \\ \text{Substitute the value of ''y'' into equation 2, we have:} \\ y=2z \\ \frac{3}{4}=2z \\ \text{Divide both sides by 2, we have:} \\ \frac{3}{4\cdot2}=\frac{2z}{2} \\ \frac{3}{8}=z \\ z=\frac{3}{8} \end{gathered}[/tex]Therefore,
ring = 1/2
heart = 3/4
hat = 3/8
