Ratio Math Problem

Question

Taylor has 3 red beads to every 8 blue beads. if there are 105 more blue beads then red beads, how many total heads does Taylor have?

Answer 1

B is the number of blue beads

R is the number of red beads

N is the TOTAL number of beads

N = R+B

B = R+105 <--- 105 more blue beads than red; save these two equations for later

Since ratio is 3 to 8, so out of every 11 beads, 3 are red and 8 are blue

3/11* N = R ---> N = (11/3)R

8/11 * N = B ---> N = (11/8)B

(11/3)R = N = (11/8)B

R/3 = B/8 <--- divides both sides by 11

8R = 3B <--- multiplies both sides by 24

R = (3/8)B

Plugs into the equation above in bold:

B = (3/8)B+ 105

(8/8)B = (3/8)B + 105

(5/8)B = 105

B = 105*8/5 = 168

this forces R=63

which forces N = R+B = 231

CHECK:

red; 63/231 = 21/77 = 3/11

blue 168/231 = 56/77 = 8/11

63 read beads

168 blue beads

213 beads altogether