the interest earned on an account varies directly with the balance in the account. if an account with a balance of $200 earns $12.50 in interest, find the amount of interest earned on an account with a balance of $500

Answer:[tex]\$31.25[/tex]Step-by-step explanation:A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]Lety-------> the interest earned on an accountx------>  the balance in the accountstep 1Find the constant k of proportionalityFor [tex]x=\$200,y=\$12.50[/tex][tex]k=y/x[/tex]substitute the values[tex]k=12.50/200=0.0625[/tex]The equation is [tex]y=0.0625x[/tex]step 2Find the amount of interest earned on an account with a balance of $500soFor  [tex]x=\$500[/tex] substitute in the equation and solve for y[tex]y=0.0625(500)=\$31.25[/tex]