DS algebraic translation practice. Sam's spending.

[tonebeeze]

I got this problem correct in seconds using intuition, but I would appreciate if someone could map out the algebra for statement one. Thanks!

Sam spends a total amount of $15000 on rent, transportation, and groceries. If she spends $9000 on rent alone, how much does she spend on groceries?

I. The amount she spends on rent exceeds the amount she spends on groceries by the same amoun as that by which the amount she spends on groceries exceeds the amount she spends on transport.

II. She spends $4000 more on groceries than on transport

OA = D

[clock60]

i`ll try to solve using math only
let be rent=r, transport=t and groceries=g
we are given that
r+t+g=15000, and r=9000
t+g=6000, and need to find g-?
(1) st 1 says that r-g=x-rent exceeds groceries on some number here-x
and g-t=x groceries exceeds transpotation on the same number x, thus
r-g=g-t
r+t=2g and r=9000
2g-t=9000, and from problem
t+g=6000
3g=15000
g=5000, so suff
(2) st 2 sems not as hard
from problem
t+g=6000, and from st
g=4000+t
2g=10000
g=5000 also suff

[tonebeeze]

Got it. the key was combining the equations:

"2g-t=9000, and from problem
t+g=6000 "

Thanks!