Together, sarah's two cats have the same mass as her dog, 11 kg. the mass of one cat is
1500 g greater than the mass of the other. what are the masses of the two cats?

First, lets do all calculations in kg. 1kg=1000 grams
Lets set 1 cat's mass as x.
Lets set the other cat's mass as y.
1) x+y=11
2) y=x+1.5   

Lets plug eq 2 into eq 1.
x+x+1.5=11
2x+1.5=11
2x=9.5
x=4.75 kg

If one cat weighs 4.75 kg, then the other must weigh 6.25 kg.

So cat1=x
cat2=y
x+y=11kg
11kg=11000g
x=y+1500
subsitute
y+1500+y=11000
subtract 1500
2y=9500
divide by 2
y=4750
subsitue
x=4750+1500
x=6250

one cat weighs 6250g and the other weighs 4750g

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

Ive seen this before! the answer is b