Ruth is eligible to claim the EIC based on Rachel $(7),$ her granddaughter and qualifying child. Rachel's mother, Petra, is also eligible and plans to claim Rachel as a qualifying child for the EIC. Rachel does not provide more than $50\%$ of her own support and lived in a home with both Ruth and Petra for the entire year. Everyone is a U$.$S$.$ citizen with social security numbers received before the due date of the return. Ruth's income, all from wages, is $$43,500.$ Petra's earned income is $$36,753.$

Which of the following statements is accurate?

Ruth may claim the EIC based on Rachel if her AGI is higher than Petra's and if she files first.

Petra holds the higher right and may claim the EIC based on Rachel because Petra is Rachel's parent.

Ruth and Petra may agree to each claim one$-$half of the EIC based on Rachel, who is a qualifying child for each of them.

As long as Ruth has a higher AGI than Petra, she may claim Rachel for purposes of the EIC.