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 :)
Regular shapes are shapes that have sides that are all equal and interior angles are also equal.
Irregular shapes are shapes that vary in the measurement of sides and interior angles.
To find the area of an irregular shape, break it down into various regular shape and individually compute its area. Add up all the area of the regular shapes formed from the irregular shape to get the area of the irregular shape.
An example of an irregular shape is the outline of a house.
Pointed roof over a square room. There are two regular shapes found in this irregular shape. A square and a triangle. Compute its individual area and add up these two areas to get the area of the house.
Answer:
r=-6
Step-by-step explanation:
Question: -3+r/3=-5
1) Multiply both sides of the equation by 3:
-9+r=-15
2) Add 9 to both sides:
r=-6
Footnotes:
1) In step 1 when I multiplied both sides of the equation by 3, don't forget you also have to multiply -3 by 3 because it is not part of the fraction (which is how I got -9)
Answer: W is your answer :)
Step-by-step explanation:
