KiaraLiedy
Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The ratio of the number of beads Karen had to the number of beads Patricia had was 2:5 .After Patricia bought another 75 beads,the ratio became 4:15.How many beads did each girl have at first?

Sagot :

naǫ
x - the number of Karen's beads
y - the number of Patricia's beads
The ratio x:y=2:5.

[tex]\frac{x}{y}=\frac{2}{5} \\ 2y=5x \\ y=\frac{5}{2}x[/tex]

Then Patricia bought another 75 beads, so the number of her beads became y+75 and the ratio became 4:15.

[tex]\frac{x}{y+75}=\frac{4}{15} \\ 4(y+75)=15x \\ y+75=\frac{15}{4}x \\ y=\frac{15}{4}x-75[/tex]

y from the first equation is equal to y from the second equation.
[tex]\frac{5}{2}x=\frac{15}{4}x-75 \\ \frac{5}{2}x-\frac{15}{4}x=-75 \\ \frac{10}{4}x-\frac{15}{4}x=-75 \\ -\frac{5}{4}x=-75 \\ x=-75 \times (-\frac{4}{5}) \\ x=-15 \times (-4) \\ x=60 \\ \\ y=\frac{5}{2}x=\frac{5}{2} \times 60=\frac{300}{2}=150[/tex]

Karen had 60 beads and Patricia had 150 beads.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.