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Third year increase: $103 500 × 1.05 = $108 675

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Therefore the profit at the end of the third year is $108 675.

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#### 108 675

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An investor splits $10 000 between two accounts: one earning 4% annual interest and the other earning 6%. If the total interest earned in one year is $520 how much was invested in each account?

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Let x be the amount invested at 4% so (10 000 - x) is invested at 6%.

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The interest equation is: 0.04x + 0.06(10 000 - x) = 520

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Simplify: 0.04x + 600 - 0.06x = 520

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Combine terms: -0.02x = -80

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Solve: x = 4 000

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Therefore $4 000 was invested at 4% and $6 000 at 6%.

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#### $4 000 at 4% $6 000 at 6%

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A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 54 meters what are the dimensions of the garden?

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Let w = width. Then length = 2w + 3.

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Perimeter = 2(length + width) = 54

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Substitute: 2((2w + 3) + w) = 54

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Simplify: 2(3w + 3) = 54 → 6w + 6 = 54

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Solve: 6w = 48 → w = 8

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Length = 2(8) + 3 = 19

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The dimensions are 8 meters (width) and 19 meters (length).

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#### 8 meters by 19 meters

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A train leaves Station A traveling at 60 km/h. Two hours later a faster train leaves Station A along the same route at 90 km/h. How far from Station A does the faster train catch up?

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Let t be the time (in hours) the faster train travels when it catches up.

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Distance traveled by first train: 60(t + 2)

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Distance traveled by second train: 90t

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Set distances equal: 60(t + 2) = 90t

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