32條F.3 GE數

1. Let $A be the original price of gasoline

So, new price of the gasoline

= A(1 + 20%)

= 1.2A

Let r% be the perentage decrease

So, 1.2A(1 – r%) = A

1.2 – 1.2r% = 1

1.2r% = 0.2

r = 50/3 %

So, the percentage decrease is 50/3 %.


2.a. Ben has $10 less than Amy

b. Let $A be the amount that Amy has

So, Ben has $(A - 10)

A = (A - 10)(1 + 10%)

A = 1.1A – 11

A = 110

So, Amy has $110 and Ben has $100.

So, the percentage

= (110 - 100)/110 X 100%

= 100/11 %

c. Let Ken has $A

then Jerry has $A(1 + 10%) = $1.1A

Billy has $A / (1 – 10%) = $10A/9 = $1.11A

So, Billy has most of the money.

1.Let E be expenditure , P be price of gasoline, Q be the consumption of gasoline
Before the increased in price: E=P*Q
After the increased in price, expenditure remains unchanged,
so E=(1+20%)P * Q1, where Q1 is the new consumption of gasoline
P*Q=(1+20%)P * Q1
Q=1.2*Q1
Q1=1/1.2 * Q
Percentage change in the consumption of gasoline=(Q1-Q)/Q *100%=-83.3%(correct to 3 sig. fig)
2a.Let Amy has $x while Ben has $y
x=y+10
y=x-10
so, Ben have $10 less than Amy
2b.From the question, x=(1+10%)y
y=1/1.1 * x
Ben have less than Amy in percentage=(x-y)/x *100%=9.09%(correct to 3 sig. fig.)
3. Let Jerry has $x, Ken has $y, Billy has $z
x=(1+10%)y, y=(1-10%)z
so, x=1.1y and y=0.9z
z=1/0.9 * y=1.11y(correct to 3 sig. fig)
Therefore, Billy has more money

1. Let $A be the original price of gasoline



So, new price of the gasoline



= A(1 + 20%)



= 1.2A



Let r% be the perentage decrease



So, 1.2A(1 – r%) = A



1.2 – 1.2r% = 1



1.2r% = 0.2



r = 50/3 %



So, the percentage decrease is 50/3 %.





2.a. Ben has $10 less than Amy



b. Let $A be the amount that Amy has



So, Ben has $(A - 10)



A = (A - 10)(1 + 10%)



A = 1.1A – 11



A = 110



So, Amy has $110 and Ben has $100.



So, the percentage



= (110 - 100)/110 X 100%



= 100/11 %



c. Let Ken has $A



then Jerry has $A(1 + 10%) = $1.1A



Billy has $A / (1 – 10%) = $10A/9 = $1.11A



So, Billy has most of the money.

1)100/120%=83.33
2a) $10,because Amy has $10 more than Ben. b)10%, the same as 2a, because Amy has 10% more than Ben.
3) Jerry, because
Jerry=x+10%+10%
Billy=x+10%
Ken=x