Algebra Know-It-ALL

which simplifies to

y= 112,500

Jane’s share was therefore $112,500. Jack got the other portion, which was 1/3 of $112,500,
or $37,500. We can also figure Jack’s share by noting that he got $150,000 − $112,500, or
$37,500.

Problem D

The old Widower Jones (who was a good friend of the old Widow Johnson) sold all his prop-
erty and put the money into a savings account. The account balance was $130,000 when he
died. He left three children: Joann, Jill, and Judy. All three are married today, and well-off.
Nevertheless, the old Widower Jones decreed, in the dullness of his demise, that Joann should
get $10,000 less than Jill, and Jill should get $20,000 less than Judy. How much did each
child get?

Solution D

Let’s say that x was the amount, in dollars, that Joann received. Then Jill got x+ 10,000 dol-
lars. Judy got (x+ 10,000) + 20,000 dollars, or x+ 30,000 dollars. We have

x+ (x+ 10,000) + (x+ 30,000) = 130,000

Ungrouping these addends and then rearranging them according to the commutative law for
addition, we obtain

x+x+x+ 10,000 + 30,000 = 130,000

which simplifies to

3 x+ 40,000 = 130,000

Subtracting 40,000 from each side gives us

3 x= 90,000

Dividing through by 3, we get

x= 30,000

That means Joann received $30,000. Jill got $10,000 more than Joann, or $40,000. Judy got
$20,000 more than Jill, or $60,000.

Word Problems 205