Question

Lisa & Ruth started a competition to see who can collect the most number of stamps. at the end of the month, the ratio of the stamps Lisa had to those Ruth had was 85:93 .Ruth collect 640 stamps in one days,then the ratio become 85:109.how many stamps Lisa had?​

Answer 1

Answer:

Number of stamps Lisa had= 3,400

Step-by-step explanation:

At the end of the month, the ratio of the stamps Lisa had to those Ruth had was 85:93.

$\frac{Lisa's stamps at End of Month}{Ruth's stamps at End of Month}$ = $\frac{85}{93}$

$\frac{Ruth's stamps at End of Month}{Lisa's stamps at End of Month}$ = $\frac{93}{85}$

On the following day Ruth collected 640 stamps.  According to the problem:

$\frac{Lisa's stamps at End of Month}{Ruth's stamps after another day's collection}$ = $\frac{85}{109}$

=> $\frac{Ruth's stamps after another days collection}{Lisa's stamps at the End of the Month}$ = $\frac{109}{85}$

=> $\frac{(Ruth's stamps at the End of the Month + 640) }{Lisa's stamps at the End of the Month}$ = $\frac{109}{85}$

=> $\frac{Ruth's stamps at End of Month}{Lisa's stamps at End of Month}$ + $\frac{640}{Lisa's stamps at End of Month}$ = $\frac{109}{85}$

=> $\frac{93}{85}$ + $\frac{640}{Lisa's stamps at End of Month}$ = $\frac{109}{85}$

=> $\frac{640}{Lisa's stamps at End of Month}$ = $\frac{109}{85}$ - $\frac{93}{85}$ = $\frac{16}{85}$

∴ Number of stamps Lisa had = $\frac{(85 x 640)}{16}$ = 3,400