KiaraLiedy
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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?

Respuesta :

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.

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