Ex. 6 To determine the height of the Aon Center Building (in Chicago), you measure the shadow cast by the building and find it to be 142 feet long. Then you measure the shadow cast by a four-foot post and find it to be 6 inches long. Estimate the building’s height.

Bldg height = post height bldg shadow post shadow

x = 48 142 6 x = 1136

Ex. 7 You invested a total of $10,000 at 4.5% and 5.5% simple interest. During 1 year, the two accounts earned $508.75. How much did you invest in each account?

Amt at 4.5% = x

Amt at 5.5% = 10000 - x

Int at 4.5% = Prt = x(0.045)(1)

Int at 5.5% = Prt = (10000 – x)(0.055)(1)

x(0.045)(1) + (10000 – x)(0.055)(1) = $508.75

-0.01x = -41.25 x = $4125 at 4.5% So $5875 at 5.5%

Ex. 8 A store has $30,000 of inventory in single-disc DVD players and multi-disc DVD players. The profit on a single-disc player is 22% and the profit on a multi-disc player is 40%. The profit for the entire stock is 35%. How much was invested in each type of DVD player?

Inv for sd = x

Inv for md = 30000 - x

Profit for sd = 0.22x

Profit for md = 0.4(30000 – x)

0.22x + 0.4(30000 – x) = 0.35(30000)

So $21,666.67 invested in md

0.22x + 0.4(30000 – x) = 105000

-0.18x = -1500

x = $8333.33 invested in sd

Ex. 9 A cylindrical can has a volume of 200 cm3 and a radius of 4 cm. Find the height of the can.

Vol = πr2h

200 = π(4)2h

h = 3.98 cm

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