Using proportions, it is found that:
a) Diana and Elsa paid $105 altogether.
b) Hannah paid Diana $21.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Hannah returned Flora $84, and Flora paid 4/5 of what Diana and Elsa paid, hence the amount Diana and Elsa received by Hannah is given as follows:
4/5x = 84
0.8x = 84
x = 84/0.8
x = 105.
Hence Diana and Elsa paid $105 altogether.
For item b, we have that the ratio of Diana and Elsa share is 1:4, hence Diana got 1/5 of the amount paid by Hannah, hence:
1/5 x 105 = 21.
Hannah paid Diana $21.
More can be learned about proportions at https://brainly.com/question/24372153
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