Emily had some red beads and blue beads in the ratio 5:2. She had 54 more red beads than blue beads. When she gave away 18 red beads, what was the new ratio of the number of red beads to that of the blue beads?
Q. Emily had some red beads and blue beads in the ratio 5:2. She had 54 more red beads than blue beads. When she gave away 18 red beads, what was the new ratio of the number of red beads to that of the blue beads?
Define Bead Numbers: Let's define the number of red beads as R and the number of blue beads as B. Given the ratio R:B=5:2 and R=B+54.
Express in Terms of x: Using the ratio, we can express R and B in terms of a common variable x, where R=5x and B=2x.
Solve for x: Substituting R=5x into the equation R=B+54, we get 5x=2x+54. Solving for x, we subtract 2x from both sides to get 3x=54. Then, x=18.
Substitute x Values: Now, substituting x=18 back into the expressions for R and B, we find R=5×18=90 and B=2×18=36.
Update Red Bead Count: Emily gave away 18 red beads, so the new number of red beads is 90−18=72.
Simplify New Ratio: The new ratio of red beads to blue beads is 72:36. Simplifying this ratio by dividing both numbers by 36, we get 2:1.
More problems from Solve proportions: word problems