Question

If Elena were to give Bonnie 20% of her money, Bonnie would have one-fourth less the amount that Elena would have after giving the money to Bonnie. If bonnie has $\$ $60.00 less than Elena, how much money, in dollars, does Elena have now?

Answer 1

Hint: In this particular question use the concept that assume any different variables be the amount of Elena and Bonnie then according to given condition construct the linear equation in terms of these variables such has it is given that Bonnie has 60 less than Elena, i.e. Amount of Bonnie is equal to the difference of the amount of Elena and $\$ 60$ so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Let Elena have $\$ $x and Bonnie have $\$ y$.
Now according to the question Elena was to give Bonnie 20% of her money.
So the remaining money Elena has = initial money Elena has – 20% of initial money Elena has.
So the remaining money Elena has = x - $\dfrac{{20}}{{100}}x$ = x – 0.2x = $\$ $0.8x
And the total money Bonnie has = initial money Bonnie has + 20% of initial money Elena has.
So, the total money Bonnie has = $\$ $ (y + 0.2x)
Now it is given that Bonnie would have one-fourth less the amount that Elena would have after giving the money to Bonnie.
So, the amount Bonnie has = Amount Elena has after given the money to Bonnie - $\dfrac{1}{4}$(Amount Elena has after given the money to Bonnie).
$ \Rightarrow y + 0.2x = 0.8x - \dfrac{1}{4}\left( {0.8x} \right)$
Now simplify we have,
$ \Rightarrow y + 0.2x = 0.6x$
$ \Rightarrow y = 0.4x$............... (1)
Now it is given that Bonnie has 60 less than Elena.
Therefore, y = x – 60................ (2)
Now substitute this value in equation (2) we have,
$ \Rightarrow x - 60 = 0.4x$
$ \Rightarrow 0.6x = 60$
$ \Rightarrow x = \dfrac{{60}}{{0.6}} = \$ 100$
So Bonnie has, y = 100 – 60 = $\$ 40$
So this is the required amount Bonnie and Elena has in dollars.

Note: Whenever we face such types of questions the key concept we have to remember is that we always recall that after constructing the equations there are lots of different methods to solve the linear equations such as elimination, substitution method etc. I have used a substitution method so solve as above we will get the required answer.