Ana earns 3x dollars per day. Beth earns 4x dollars per day.
Charlize earns 75% more than Ana. Diana earns 30% less than Beth.
Charlize earns $147 more than Diana. Work out how much money each person gets
Answers
Step-by-step explanation:
Given :-
Ana earns 3x dollars per day. Beth earns 4x dollars per day.Charlize earns 75% more than Ana. Diana earns 30% less than Beth.Charlize earns $147 more than Diana.
To find :-
How much money each person gets ?
Solution :-
Money earned by Ana per day = $ 3X
Money earned by Charlize = 75% more than Ana
=> $3X + 75% of $3X
=> 3X +(75% × 3X)
=> 3X +[(75/100)×3X]
=> 3X+[(3/4)×3X]
=> 3X+[(3×3X)/4]
=> 3X +(9X/4)
=> (12X+9X)/4
=>21X/4
Money earned by Charlize = $ 21X/4
Money earned by Beth = $ 4X
Money earned by Diana = 30% less than Beth
=> 4X -(30% of 4X)
=> 4X -(30% × 4X)
=> 4X -[(30/100)×4X]
=> 4X -[(3/10)×4X]
=> 4X-(12X/10)
=> 4X -(6X/5)
=> (20X-6X)/5
=> 14X/5
Money earned by Diana = $ 14X/5
Given that
Charlize earns $147 more than Diana
=> 21X/4 = (14X/5) + 147
=> (21X/4)-(14X/5) = 147
LCM of 4 and 5 = 20
=> [(21X×5)-(14X×4)]/20 = 147
=> (105X - 56X)/20 = 147
=> 49X /20 = 147
=> 49X = 147×20
=> 49X = 2940
=> X = 2940/49
=> X = 60
The value of X = $ 60
Money earned by Ana = 3X
=> 3×$60 = $ 180
Money earned by Beth = 4X
=> 4×$60 = $ 240
Money earned by Diana = $14X/5
=> 14×60/5
=> 14×12
=> $ 168
Money earned by Charlize = Diana + $ 147
=> $ 168 + $ 147
=> $ 315
Answer:-
Ana earns $ 180 ,
Beth earns $ 240 ,
Charlize earns $ 315,
Diana earns $ 168
Check:-
Charlize earns 75% more than Ana.
=> 180+ (75% × 180)
=>180+ (75/100)×180
=>180+ ( (3/4)×180)
=> 180+(3×45)
=> 180+135
=>$ 315
Diana earns 30% less than Beth.
=> 240-(30% of 240)
=> 240-[(30/100)×240]
=> 240-[(3/10)×240]
=>240-[3×24]
=> 240-72
=> $ 168
Verified the given relations in the given problem.