Math 101-06

9-27-2017

* [Systems word problems]*

1. How many pounds of nuts worth $2.40 per pound must be mixed with raisins worth $1.50 per pound to obtain 36 pounds of a mixture worth $2.00 per pound?

Let x be the number of pounds of nuts and let y be the number of pounds of raisins.

The first and third columns give the equations

Multiply the first equation by 2.4 and subtract the second equation:

Hence, . Thus, 20 pounds of nuts and 16 pounds of raisins are needed for the mixture.

2. How many liters of a salt solution and a salt solution must be mixed to obtain 40 liters of a salt solution?

Let x be the number of liters of the salt solution and let y be the number of liters of the salt solution.

The first and third columns give the equations

Multiply the first equation by 0.2 and subtract it from the second:

Then , so .

Use 30 liters of the salt solution and 10 liters of the salt solution.

3. $1100 is divided among two accounts. The first account pays 3% interest, while the second account pays 4% interest. At the end of one interest period, the two accounts have returned a total of $41 in interest. How much was invested in each account?

Let x be the amount invested in the first account, and let y be the amount invested in the second account.

The first and third columns give two equations:

Multiply the first equation by 0.03 and subtract it from the second:

Then . Thus, $300 was invested in the first account and $800 was invested in the second account.

4. $1100 is divided between two accounts. The first account pays interest, while the other pays interest. After one interest period, the interest earned by the account is $13 greater than the interest earned by the account. How much was invested in each account?

Let x be the amount invested in the account, and let y be the amount invested in the account.

The first column gives .

The interest earned by the account is $13.0 greater than the interest earned by the account, so from the third column I get

Multiply by 0.03 and subtract :

Then . Thus, $700 was invested in the account, and $400 was invested in the account.

*There is no security in life, only opportunity.* - *Mark
Twain*

Copyright 2017 by Bruce Ikenaga