Wednesday 26 October 2011

A. a "5 x 7" picture is enlarged to "8 x 10". By what percent did it's area change?

B. Selena has a meter cube box filled with 1 centimeter cubes. 2.7% of these cubes are solid gold. What size cube would she need to hold only the gold cubes?



C.Daniel's age is 15% of Sarah's. Luke's age is 75% of Sarah's and Rachel's is 300 of Daniel's. Added together,their ages total 141. How old is Rachel?
A. a %26quot;5 x 7%26quot; picture is enlarged to %26quot;8 x 10%26quot;. By what percent did it's area change?
A. A = 5*7 = 35 u^2

A' = 8*10 = 80 u^2



% change in area from A to A': (80 - 35)/35



B. because 1 m^3 = 10^6 cm^3, therefore the box contains a total of 1 million cubes, the number of gold cubes equal: 0.027*10^6 = 27000 gold cubes, cube root this to get 30 cm. So the side length of your gold cube container is 30cm.



C. A(D) = 0.15 A(S)

A(L) = 0.75 A(S)

A(R) = 3 A(D)

A(S + D + L + R) = 141

A(R) = ?



Convert A(R) to age in terms of A(S)

so A(R) = 3 A(D) = 3 [0.15 A(S)] = 0.45 A(S)



Now solve for A(D + L + R).



A(S + D + L + R) = (1 + 0.15 + 0.75 + 0.45) A(S) = 2.35 A(S) = 141

A(S) = 60



So A(R) = 3 [0.15*60) = 27



Answer: Rachel is 27 years old.