We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.
PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE
Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5
So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5
Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20
So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25
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<span>Finally, we check our solution against the original question. </span>
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔
Hope that helped :)
Answer:
Let no be x
algebraic expression =x-5
Step-by-step explanation:
Answer:
28.8sq area is the area of the prism
Step-by-step explanation:
2.4x1.5x8
Answer:
The rate of interest is 20% and the sum is $3,750
Step-by-step explanation:
In order to calculate the sum and rate of interest we would have to make the following calculation:
rate of interest= (sum in 4 years-sum in 3 years)*100/sum in 3 years*1
According to the given data we have the following:
sum in 4 years=$7,776
sum in 3 years=$6,480
Therefore, sum in 4 years-sum in 3 years=$7,776-$6,480=$1,296
Therefore, rate of interest=$1,296*100/$6,480*1
rate of interest=20%
To calculate the sum we would have to make the following calculation:
FV=PV(1+20%)∧3
$6,480=PV(1,20)∧3
PV=$3,750
Sum is $3,750
Direct variation is
y=kx
subsitute
-6=-36k
diivde both sdies by -36
1/6=k
the equation is
y=1/6x or B
