All 303 families

GB-16-06-001 · Changing ratios

The ratio of red beads to blue beads is 13 : 16. When 24 red beads are added, the numbers of red and blue beads are equal. Work out how many beads there were originally.

Ratio: Using ALGEBRAIC Fractions (Changing Ratios) Booklet p. 20
Method
1) Write the original ratio with x
2) Write the change
3) Equate to the new ratio as fractions
4) Cross multiply and solve
5) Find the requested quantity
Worked Example (GB-16-06-001)
1)
Write the original ratio with x: red=13x,blue=16x\mathrm{red}=13x,\quad\mathrm{blue}=16x.
2)
Write the changed ratio: (13x+24):16x(13x+24):16x.
3)
The new ratio is 1:11:1. Rewrite as fractions: 13x+2416x=11\frac{13x+24}{16x}=\frac11.
4)
Cross multiply and solve: 13x+24=16x⇒3x=24⇒x=813x+24=16x\Rightarrow 3x=24\Rightarrow x=8.
5)
Find the original total: (13+16)(8)=232(13+16)(8)=232 beads.
Ans = 232