# Four Unknowns, Three Equations

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems > Many Variables## Four Unknowns, Three Equations

Find the sum of x, y, z, and w if

3x + y = 170

y + 3z = 50

z + x - 2w = 30

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### Blowing Bubbles

Each of five children blow some bubbles. The number of bubbles blown by the first child equals the number of bubbles blown by the second and third children combined. The number of bubbles blown by the second child is ten less than the number of bubbles blown by the third and fourth children combined. The number of bubbles blown by the third child is the number of bubbles blown by the fifth child, minus the number of bubbles blown by the fourth child. If the fifth child blew 32 bubbles, how many bubbles were blown by the first and fourth children combined?

### Picking Apples

While visiting an orchard, my son picked some apples, and so did my daughter. Together, they picked as many apples as I did. The three of us together picked as many apples as my wife. If my wife gave me a third of her apples, I would have sixteen more apples than her. How many apples did we pick in all?

### All the Letters

Let a, b, c,...x, y, z be variables such that:

- Every consonant that is preceded by a vowel is two less than twice the value of that vowel.
- Every consonant that is preceded by another consonant is twice the value of that consonant.
- Every vowel is one sixteenth the value of the consonant preceding it.

Write z in terms of a.

### Hermie goes Christmas Shopping

Hermie the Elf wants to buy Christmas gifts for the students in his dentistry class. Unfortunately, he only has coins - pennies, nickels, dimes, and quarters. In all, he spends twice as many nickels as quarters, four more dimes than nickels, and the number of pennies was seven less than the total of his nickels, dimes and quarters.

In all, he spent $4.57. How many coins did he spend?

### Thanksgiving Family Gathering

When Thanksgiving arrives, my house is filled with family, gathering from around the country for Thanksgiving dinner. It's tough to keep track of all the people.

There are five times as many grandchildren as there are daughters-in-law.

The number of grandchildren, plus the number of daughters isFor every son except one there is a daughter-in-law, and there are three more daughters than sons-in-law.

I have twice as many sons as daughters.

Aside from all these people, there is also me, my wife, and 34 great-grandchildren.

How many people are at the family gathering?

### A Kranky Christmas

This year Mr. Krank spent three times as much money on gifts for family members as he did on gifts for co-workers. The amount of money he spent on Christmas decorations was $150 less than the amount of money he spent on Christmas cards. The amount he spent on Christmas charities exceeded the combination of co-worker gifts and Christmas card expense by 20%. In addition to all of this, a third of the total spent on Christmas was expenses related to their famous Christmas-Eve party. If the Kranks had not purchased any Christmas gifts, they would have spent $1983 on Christmas. If, instead, they had chosen to give gifts but skip the Christmas cards, they would have spent $2673 in all.

If the Kranks skipped Christmas altogether, how much money would they have saved?

### Buying Christmas Gifts

Lauren, Martha, Jake and Judah all decide to buy Christmas gifts for each other.

Lauren spends $5 more than Martha. Martha spends twice as much as Jake, Jake spends $17 less than Judah, and Judah spends $15 less than Lauren and Martha combined.

How much money did they spend altogether?