Devi bought some red and blue beads to make necklace. The ratio of the number of red beads to the number of blue beads is 3:5. After making the necklace, the ratio of the number of red beads to the number of blue beads became 2:5. A total of 21 red beads and 2/3 of the blue beads were used to make the necklace.
How many red and blue beads did Devi buy altogether?
Please help!
r/b = 3/5
(r-21)/(b/3) = 2/5
now work your magic. be sure to check your answer.
Please help, does this calculation looks right?
r-21 x 3/b= 2/5
r-21x15=2b
r-315=2b I'm stuck????
To solve this problem, we can start by setting up a system of equations.
Let's denote the number of red beads as "r" and the number of blue beads as "b."
According to the problem, the ratio of the number of red beads to the number of blue beads is initially 3:5. This can be expressed as:
r/b = 3/5 -----> Equation 1
After making the necklace, the ratio of the number of red beads to the number of blue beads becomes 2:5. This can be expressed as:
(r - 21) / (b - 2/3b) = 2/5 -----> Equation 2
Now, let's solve the equations:
From Equation 1, we can re-arrange it to find r in terms of b:
r = (3/5) * b
Substituting this expression for r into Equation 2, we get:
((3/5) * b - 21) / (b - 2/3b) = 2/5
Simplifying this equation, we can cross-multiply:
5 * ((3/5) * b - 21) = 2 * (b - 2/3b)
Expanding and simplifying:
3b - 105 = 2b - 4/3b
Multiplying through by 3 to eliminate fractions:
9b - 315 = 6b - 4b
Combining like terms:
9b - 6b + 4b = 315
7b = 315
Solving for b:
b = 315 / 7
b = 45
Substituting this value of b back into Equation 1:
r = (3/5) * 45
r = 27
Therefore, Devi bought a total of 27 red beads and 45 blue beads.