Word Problem

classic Classic list List threaded Threaded
3 messages Options
Joe Joe
Reply | Threaded
Open this post in threaded view
|

Word Problem

Hi help needed for this word problem:

Alicia and Clara had a total of 764 beads. They each used some of their beads to make a necklace each and keep the remaning beads. Alicia had 1/3 as many beads remaining as Clara after making their necklaces. The no. of beads Clara used to make her necklace was 63 more than what she had left. Clara used 3 times as many beads as Alicia to make her necklace.
\
a) How many beads were used to make the 2 necklaces?
b) How many beads did Alicia have at first?
AlgebraHouse AlgebraHouse
Reply | Threaded
Open this post in threaded view
|

Re: Word Problem

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
Joe Joe
Reply | Threaded
Open this post in threaded view
|

Re: Word Problem

Thanks a lot.