Acollege student earned $5400 during summer vacation working as a waiter in a restaurant on the boardwalk at the beach. the student invested part of the money at 8% and the rest at 6%. if the student received a total of $370 in interest at the end of the year, how much was invested at 8%?

He invested $2300 at 8%

Step-by-step explanation:

* Lets explain how to solve the problem

- The student earned $5400

- He invested some of them at 8% and the rest at 6%

- He received from both a total $370 in interest at the end of the year

- The rule of the interest is I = Prt , where

# I is the interest

# P is the money invested

# r is the rat (in decimal)

* Lets change these information to equations

- Let the student invested $x at 8% and the rest at 6%

∵ The total investment in the two accounts is 5400

∵ He invested $x in the first account (8%)

∴ He invested $(5400 - x) in the second account (6%)

- Lets calculate the interest for each account I1 for first account of rate

 8% and I2 for the second account of rat 6%

∵ I1 = Prt

∵ P = x and t = 1

∵ r = 8/100 = 0.08

∴ I1 = x(0.08)(1) = 0.08x

∵ I2 = Prt

∵ P = (5400 - x) and t = 1

∵ r = 6/100 = 0.06

∴ I2 = (5400 - x)(0.06)(1) = 5400(0.06) - x(0.06) = 324 - 0.06x

- The student received a total of $370 in interest at the end of the

  year from both accounts

∴ I1 + I2 = 370

Substitute the values of I1 and I2 in the equation

∴ 0.08x + (324 - 0.06) = 370

- Collect the like terms

∴ (0.08 - 0.06) + 324 = 370

∴ 0.02x + 324 = 370

- Subtract 324 from both sides

∴ 0.02x = 46

- Divide both sides by 0.02

∴ x = 2300

∵ x is the money invested in the account of 8%

∴ He invested $2300 at 8%

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