Question

rani had 216 more blue beads than green beads at first. after she bought some additional beads, the number of blue reads increased by 25% and the number og green beads increased by 50%. if rani had bought 14 more blue beads than green beads, how many blue beads would she have in the end?

Answer 1

Let's set up the equations to solve the problem step by step:

Let's assume Rani had x green beads at first. Then she had (x + 216) blue beads.

After buying additional beads:

The number of blue beads increased by 25%, which means she bought 0.25 * (x + 216) more blue beads.

The number of green beads increased by 50%, which means she bought 0.5 * x more green beads.

According to the given information, she bought 14 more blue beads than green beads. So, we can set up the equation:

0.25 * (x + 216) = 0.5 * x + 14

Now, let's solve for x:

0.25x + 54 = 0.5x + 14

0.5x - 0.25x = 54 - 14

0.25x = 40

x = 40 / 0.25

x = 160

So, Rani had 160 green beads at first.

Now, to find the number of blue beads at the end, we need to add 216 (initial difference) + 25% increase:

Number of blue beads at the end = (x + 216) + 0.25 * (x + 216)

Number of blue beads at the end = 160 + 216 + 0.25 * (160 + 216)

Number of blue beads at the end = 160 + 216 + 0.25 * 376

Number of blue beads at the end = 160 + 216 + 94

Number of blue beads at the end = 470

So, Rani would have 470 blue beads in the end.