Math Is Fun Forum

momofmathkid

Member

Registered: 2008-01-14

Posts: 32

Guess and Check Algebra

It looks like my dear daughter actually has 3 problems to complete, and I can't help her...oh my!  Here's the 2nd problem:

On a string of 15 opals, the center stone is the largest and the most expensive.  Starting from one end, including the center stone, each opal is worth $50 more than the previous one.  Starting at the other end and including the center stone, each opal is worth $25 more than the previous one.  The total value of the 15 opals is $4,650.  What is the value of the center opal?

Any help or insight that you can provide today is appreciated!

Mom of Math Kid

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Guess and Check Algebra

let the centre stone be 'x'

either side of the centre stone you will 7 stones, with values of:

x - 7×50, x - 6×50 ... x - 50, x, x - 25 ... x - 6×25, x - 7×25    etc for the rest

the ones on the left can be written as x - n×50, and ones on the right as x - n×25, with n from 1 to 7

you can then write the sum of all stones as being:

which simplified is:

you can evaluate that by hand if you do not know the formula for the sum, otherwise it is:

since the total sum is given as 4650, 15x - 2100 = 4650, 15x = 6750, x = 450

so the centre stone is worth $450

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