5. Lorna, Rita, and Mirna together saved 750 kn. We know that Rita saved three times more than three quarters of Lorna's amount, and Mirna's savings are $85 \mathrm{kn}$ more than two thirds of Rita's savings. How much did each of them save?

## COUNTY COMPETITION IN MATHEMATICS
5. Lorna, Rita, and Mirna together saved $750 \mathrm{kn}$. We know that Rita saved three times more than three quarters of Lorna's amount, and Mirna's savings are $85 \mathrm{kn}$ more than two thirds of Rita's savings. How much did each of them save?

## Solution.

The amount saved by Lorna is represented by a column.

Since Rita saved three times more than three quarters of Lorna's amount, we will divide Lorna's amount into 4 equal parts to get the quarters.

One of these parts represents $x$ kuna.

$1 \mathrm{POINT}$

Rita's amount will be represented by a column that is 3 times higher than three quarters of Lorna's, i.e., $9 x$ kuna.

$1 \mathrm{POINT}$

Mirna's amount will be represented by a column that is equal to two thirds of the column representing Rita's amount (6x kuna) and adding $85 \mathrm{kn}$ to it.

$1 \mathrm{POINT}$

![](https://cdn.mathpix.com/cropped/2024_05_30_5cfeb7f7e539b150a939g-10.jpg?height=377&width=1077&top_left_y=925&top_left_x=247)

Lorna has $4 x$ kuna, Rita has $9 x$ kuna, and Mirna has $(6 x+85)$ kuna.

It holds that $4 x+9 x+(6 x+85)=750$.

$1 \mathrm{POINT}$

Simplifying the equation, we get $19 x+85=750, \quad 1$ POINT

$\begin{array}{ll}\text { and further solving } 19 x=665, & 1 \mathrm{POINT}\end{array}$

from which it follows that $\quad x=35 . \quad 1$ POINT

Lorna has 4 $\cdot$ 35 kuna, i.e., 140 kn, 1 POINT

Rita has $9 \cdot 35$ kuna, i.e., 315 kn, 1 POINT

and Mirna has $(6 \cdot 35+85)$ kuna, i.e., 295 kn. 1 POINT

TOTAL 10 POINTS

## COUNTY COMPETITION IN MATHEMATICS  March 29, 2021.