# Solutions to Problem Set 9

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.

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