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24 Dec 2025, 08:04
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Bookmarks
AA = Alex afternoon
AE = Alex evening
MA = Maya afternoon
ME = Maya evening
prices:
4(AA+MA) + 6(AE+ME) = 1800
AA=2ME -> ME=AA/2
AE=2MA -> MA=AE/2
4(AA+AE/2) + 6(AE+AA/2) = 1800
4AA+2AE+6AE+3AA = 1800
7AA+8AE = 1800
Alex Total = AT = AA + AE -> AE = AT-AA
Substituting:
7AA+8AE = 1800
7AA+8(AT-AA) = 1800
7AA+8AT-8AA = 1800
AA=8AT-1800
Checking values:
+ AT=120 -> AA=-840 -> impossible
+ AT=180 -> AA=-360 -> impossible
+ AT=240 -> AA=120 -> AE=240-120=120 -> ME=AA/2=60 -> MA=AE/2=60
Afternoon Total = AA+MA=180 -> possible
Alex Total=240 and Afternoon Total=180
AE = Alex evening
MA = Maya afternoon
ME = Maya evening
prices:
4(AA+MA) + 6(AE+ME) = 1800
AA=2ME -> ME=AA/2
AE=2MA -> MA=AE/2
4(AA+AE/2) + 6(AE+AA/2) = 1800
4AA+2AE+6AE+3AA = 1800
7AA+8AE = 1800
Alex Total = AT = AA + AE -> AE = AT-AA
Substituting:
7AA+8AE = 1800
7AA+8(AT-AA) = 1800
7AA+8AT-8AA = 1800
AA=8AT-1800
Checking values:
+ AT=120 -> AA=-840 -> impossible
+ AT=180 -> AA=-360 -> impossible
+ AT=240 -> AA=120 -> AE=240-120=120 -> ME=AA/2=60 -> MA=AE/2=60
Afternoon Total = AA+MA=180 -> possible
Alex Total=240 and Afternoon Total=180
24 Dec 2025, 08:04
Kudos
Bookmarks
Alex (A) and Maya (M)
Afternoon copy = $4
Evening copy = $6
A(a) = 2*M(e)
M(a) = 1/2*A(e) => 2M(e) = A(e)
Now 4[A(a) + Ma(a)] + 6[A(e) + M(e)] = 1800
=> 4*[2M(e) + 1/2 * A(e)] + 6[A(e) + M(e)] = 1800
=> 14M(e) + 8A(e) = 1800
=> 7M(e) + 4A(e) = 900
Taking integer values, we try A(e) = 120
=> 7M(e) + 480 = 900
=> 7M(e) = 420
=> M(e) = 60
Now A(a) = 2M(e) = 2*60 = 120
M(a) = 1/2 * A(e) = 120/2 = 60
Alex Total = A(a) + A(e) = 120 + 120 = 240
Afternoon Total = A(a) + M(a) = 120 + 60 = 180
Afternoon copy = $4
Evening copy = $6
A(a) = 2*M(e)
M(a) = 1/2*A(e) => 2M(e) = A(e)
Now 4[A(a) + Ma(a)] + 6[A(e) + M(e)] = 1800
=> 4*[2M(e) + 1/2 * A(e)] + 6[A(e) + M(e)] = 1800
=> 14M(e) + 8A(e) = 1800
=> 7M(e) + 4A(e) = 900
Taking integer values, we try A(e) = 120
=> 7M(e) + 480 = 900
=> 7M(e) = 420
=> M(e) = 60
Now A(a) = 2M(e) = 2*60 = 120
M(a) = 1/2 * A(e) = 120/2 = 60
Alex Total = A(a) + A(e) = 120 + 120 = 240
Afternoon Total = A(a) + M(a) = 120 + 60 = 180
Bunuel
24 Dec 2025, 08:05
Kudos
Bookmarks
Based on what we know,
Let,
Alex afternoon sales = a
Alex evening sales = b
Maya afternoon sales = m
Maya evening sales = n
Alex sold twice in afternoon as maya sold in evening
=> a = 2n
Maya sold half as many in afternoon as Alex sold in evening
=> m = b/2
=> b = 2m
Afternoon price of booklet = 4
Evening price of booklet = 6
We need to find Alex total number of booklets sold and Afternoon total number of booklets sold
=> We need
Alex total = a +b = 2n + b ----- (1)
Afternoon total = a + m = 2n + b/2
Total revenue = 4*(a + m) + 6*(b+n) = 1800
=> 4*(2n + b/2) + 6*(b+n) = 1800
=> 4b+7n = 900 ------ (2)
Now we substitute the values in the table for Alex total in (1) and with (2) we try solving,
Alex Total = 230
2n + b = 230
4b + 7n = 900
=> b = 190 and n = 20
Afternoon total = 2n + b/2 = 40 + 95 = 135 which is not there
Alex Total = 240
2n + b = 240
4b + 7n = 900
=> b = 120 and n = 60
Afternoon total = 2n+b/2 = 120 + 60 = 180 which is there in the table
Alex Total = 240
Afternoon total = 180
Let,
Alex afternoon sales = a
Alex evening sales = b
Maya afternoon sales = m
Maya evening sales = n
Alex sold twice in afternoon as maya sold in evening
=> a = 2n
Maya sold half as many in afternoon as Alex sold in evening
=> m = b/2
=> b = 2m
Afternoon price of booklet = 4
Evening price of booklet = 6
We need to find Alex total number of booklets sold and Afternoon total number of booklets sold
=> We need
Alex total = a +b = 2n + b ----- (1)
Afternoon total = a + m = 2n + b/2
Total revenue = 4*(a + m) + 6*(b+n) = 1800
=> 4*(2n + b/2) + 6*(b+n) = 1800
=> 4b+7n = 900 ------ (2)
Now we substitute the values in the table for Alex total in (1) and with (2) we try solving,
Alex Total = 230
2n + b = 230
4b + 7n = 900
=> b = 190 and n = 20
Afternoon total = 2n + b/2 = 40 + 95 = 135 which is not there
Alex Total = 240
2n + b = 240
4b + 7n = 900
=> b = 120 and n = 60
Afternoon total = 2n+b/2 = 120 + 60 = 180 which is there in the table
Alex Total = 240
Afternoon total = 180
