x = number of beads Clara had left

x/3 = number of beads Alicia had left {Alicia had 1/3 as many remaining as Clara}

x + 63 = number of beads Clara used {Clara used 63 more than what she had left}

(x + 63)/3 = number of beads Alicia used {Clara used 3 times Alicia, therefore Alicia's used is Clara's divided by 3}

All of the beads, used and left, add up to 764.

x + (x/3) + (x + 63) + [(x + 63)/3] = 764 {added up amounts, used and left, and set equal to 764}

3x + x + 3x + 189 + x + 63 = 2292 {multiplied entire equation by 3 to eliminate fractions}

8x + 252 = 2292 {combined like terms}

8x = 2040 {subtracted 252 from each side}

x = 255 {divided each side by 8}

**Used to make:**x + 63 = 318 by Clara

(x + 63)/3 = 106 by Alicia

=

**424 total****Alica had at first:**x/3 = 85

(x + 63)/3 = 106

=

**191 total ***- Algebra House*
**
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