Cindy had twice as many funfair tickets for sale as Johnson. After she sold 70 tickets and Johnson sold 20 tickets, they had the same number of tickets left.
What was the total number of tickets both of them had for sale at first?
Answers
Gɪᴠᴇɴ :-
- Cindy had twice as many funfair tickets for sale as Johnson. After she sold 70 tickets and Johnson sold 20 tickets, they had the same number of tickets left.
ᴛᴏ ғɪɴᴅ :-
- Total number of Tickets of Cindy and Johnson
sᴏʟᴜᴛɪᴏɴ :-
Let number of tickets of Cindy be x and Johnson be y,
then,
➥ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ 1sᴛ - Cᴏɴᴅɪᴛɪᴏɴ :-
➠ x = 2y. --(1)
➥ ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ 2nd - Cᴏɴᴅɪᴛɪᴏɴ :-
➠ x - 70 = y - 20
➠ x - y = 70 - 20
➠ ( x - y) = 50 --(2)
Substitute value of x from (1) in (2) , we get,
➠ x - y = 50
➠ 2y - y = 50
➠ y = 50
Put y = 50 in (1) , we get,
➠ x = 2y
➠ x = 2×50
➠ x = 100
Hence,
Numbers of Tickets of :-
- Cindy = x = 100
- Johnson = y = 50
Given
Cindy had twice as many funfair tickets for sale as Johnson. After she sold 70 tickets and Johnson sold 20 tickets, they had the same number of tickets left.
To find
What was the total number of tickets both of them had for sale at first?
Solution
★Let the Johnson had ticket be x then Cindy had ticket be y
✞According to the given condition
✰Cindy had twice as many funfair tickets for sale as Johnson
- 2y = x
✰After she sold 70 tickets and Johnson sold 20 tickets, they had the same number of tickets left.
- (x - 70) = (y - 20)
→ x - 70 = y - 20
→ x - y = 70 - 20
→ x - y = 50
✞ Substitute the value of x in eqⁿ (ii)
→ x - y = 50
→ 2y - y = 50
→ y = 50
✞ Now substitute the value of y in eqⁿ (i)
→ 2y = x
→ x = 2*50 = 100
Hence,
Total number of tickets Cindy had
= x = 100
Total number of tickets Johnson had
= y = 50