Algebra Know-It-ALL

204 First-Degree Equations in One Variable

Problem B

The old Widow Johnson sold all her property and put the cash into a savings account.

The account contained $150,000 when she died. She left two children: Jane and Jack.

Jane got married and then, like her mother, became a widow. Jane has two children to

support now, and Jack is a bachelor living alone. Knowing that Jane would likely need

more money than Jack, the old Widow Johnson, in the wisdom of her waning weeks,

decided that Jane ought to get three times as much of the inheritance as Jack. How much

did each child get?

Solution B

Let’s call Jack’s share of the inheritance, in dollars, x.Then Jane got 3x. The total inheritance,

in dollars, was 150,000. Therefore,

x+ 3 x= 150,000

We can simplify this to

4 x= 150,000

Then we divide through by 4 to get

x= 37,500

Therefore, Jack received $37,500. Jane got the other portion of the inheritance. That

was 3 × $37,500, or $112,500. We can also figure Jane’s share by noting that she got

$150,000− $37,500, or $112,500.

Problem C

Solve the previous problem by letting y represent Jane’s share of the inheritance, in dollars,

rather than Jack’s share.

Solution C

If we call Jane’s share of the inheritance y, in dollars, then Jack’s share was y/3. When we set

up the equation on this basis, we get

y+y/3= 150,000

which can be simplified to

(4/3)y= 150,000

If we multiply through by 3/4, we get

(3/4)(4/3)y= 3/4 × 150,000