Question

un elev are o suma de bani .
In prima zi cheltuie 1/3 +inca10 lei din suma.
A doua zi cheltuie 2/3 din rest +inca 5lei.
A treia zi cheltuie cu 7 lei mai mult decat 1/9 din noul rest si ii mai raman 33 de lei.
Ce suma a avut elevul si cat a cheltuit in fiecare zi.

Answer 1

x=suma de bani
x/3+10=ziua 1
x-x/3-10=2x/3-10=rest
2/3(2x/3-10)+5=4x/9-20/3+5=4x/9-5/3=ziua 2
2x/3-10-4x/9+5/3=2x/9-25/3=rest
1/9(2x/9-25/3)+7=2x/81-25/27+7=2x/81+164/27
x/3+10+4x/9-5/3+2x/81+164/27+33=x
27x+810+36x-135+2x+492+2673=81x
16x=3840
x=240 lei
ziua 1     240x1/3+10=90 lei
rest        240-90=150 lei
ziua 2     150x2/3+5=105 lei
rest        150-105=45 lei
ziua 3     45x1/9+7=12 lei
rest        45-12=33 lei

Answer 2

x=suma de bani
Prima zi :=(1/3)*x+10=x/3+10

a doua zi 2/3 din rest, dar restul este egal cu : x-(x/3+10)=2x/3-10
a doua zi : 2/3(2x/3-10)+5=4x/9-20/3+5=4x/9-5/3

rest: 2x/3-10-4x/9+5/3=2x/9-25/3=

a treia zi : 1/9(2x/9-25/3)+7=2x/81-25/27+7=2x/81+164/27


x/3+10+4x/9-5/3+2x/81+164/27+33=x

27x+810+36x-135+2x+492+2673=81x

16x=3840

x=240 lei

verificare

ziua1 +ziua 2+ziua 3+33=240

ziua 1    x/3+10= 240×1/3+10=90

ziua 2     2x/3-10=150×2/3+5=105

ziua 3   2x/81+164/27=  45×1/9+7=12

ziua1 +ziua2+ziua 3+33=240

90+105+12+33=240

240=240