Answered

Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Sagot :

Naǫidn
x - the number of red jelly beans
y - the number of yellow jelly beans

The ratio of red jelly beans to yellow jelly beans is 3:4.
[tex]\frac{x}{y}=\frac{3}{4} \ \ \ |\times y \\ x=\frac{3}{4}y[/tex]

If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5.
[tex]\frac{x-3}{y-6}=\frac{4}{5} \ \ \ |\hbox{cross multiply} \\ 5(x-3)=4(y-6) \\ 5x-15=4y-24 \ \ \ |+15 \\ 5x=4y-9 \ \ \ |\div 5 \\ x=\frac{4}{5}y-\frac{9}{5}[/tex]

[tex] x=x \\ \frac{3}{4}y=\frac{4}{5}y-\frac{9}{5} \\ \frac{3}{4}y-\frac{4}{5}y=-\frac{9}{5} \\ \frac{15}{20}y-\frac{16}{20}y=-\frac{9}{5} \\ -\frac{1}{20}y=-\frac{9}{5} \ \ \ |\times (-20) \\ y=-\frac{9}{5} \times (-20) \\ y=9 \times 4 \\ y=36 [/tex]

There were 36 yellow jelly beans in the dish.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.