Question 622104
1. {{{y=2x+1}}}
2. For the corn, the area (in square feet) is
{{{A=12*(2x+1)=24x+12}}}
3. {{{length=2x+1-3=2x-2=2(x-1)}}}
4. For the pea bed, the area (in square feet) is
{{{A=(2*(x-1))^2=4(x^2-2x+1)=4x^2-8x+4}}}
5. The total garden area (in square feet) is
{{{A=4x^2-8x+4+24x+12=4x^2+16x+16=4(x^2+4x+4)}}}
6. How many rows of corn can Gina plant if she wants to make the total area of the two beds 400 square feet?
{{{4(x^2+4x+4)=400}}} --> {{{x^2+4x+4=100}}} --> {{{x^2+4x-96=0}}}
Factoring,
{{{x^2+4x-96=0}}} --> {{{(x+8)(x-12)=0}}} --> {{{x=12}}} or {{{x=-8}}}
Of course, -8 rows of corn does not make sense, so
{{{highlight(x=12)}}} rows of corn.
7. For the corn {{{y=2-12+1=highlight(25)}}} feet is the space needed for 12 rows, and the corn portion of the garden was to be 12 feet long (according to part 2 of the problem). So the corn area is 25 feet by 12 feet.
The pea garden is 3 feet less in length that the 25 feet from part 1 (with the x=12 from part 7). That is
{{{35-3=highlight(22)}}} feet, and it is square. It measure 22 feet by 22 feet.
8. Assuming that the wood has to fully encase each section of the garden (no adjoining sections and skipping the fence in between), we need to encase a 25 foot by 12 foot rectangle and a 22 foot by 22 foor square. The perimeters are
{{{P=25*2+12*2=74}}} feet for the corn and
{{{P=4*22=88}}} feet for the peas.
The total length is {{{74+88=highlight(162)}}} feet.
PART B
1. ${{{0.17*2000000}}}=${{{340000}}}=${{{3.4*100000}}}=${{{3.4*10^5}}}
2. ${{{421000}}}=${{{4.21*100000}}}=${{{4.21*10^5}}}
3. The increase is
${{{4.21*10^5}}}-${{{3.4*10^5}}}=${{{(4.21-3.4)*10^5}}}=${{{0.81*10^5}}}
As a fraction of ${{{3.4*10^5}}} , That amounts to
{{{0.81*10^5/(3.4*10^5)=0.81/3.4=0.238}}} (rounded)
That fraction (0.238 as decimal) is 23.8/100=23.8% as a percentage