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Inga [223]
3 years ago
11

The sum of 2 numbers is 44 the smaller number is 16 less than the larger number what are the numbers

Mathematics
1 answer:
Anon25 [30]3 years ago
4 0
X=27 and y=11
if you let each number equal x and y we know the sum is 38 so x+y=38
and the smaller is 16 less than the larger
. so if we say the smaller number is 7 then x-16=y
these can be solved as a simultaneous equation. x+(x-16)=38
2x-16=38
2x=54
x=27
(27)-16=y
y=11
so the answer is x=27 y=11
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The 12th term of a sequence is 41 and the 15th term is 140. What is the nth term?
OLga [1]
An= mth term.
an=a₁+(n-1)*d

a₁₂=41
a₁₅=140

a₁₂=41
41=a₁+(12-1)*d
41=a₁+11d 
a₁+11d=41    (1)

a₁₅=140
140=a₁+(15-1)*d
140=a₁+14d 
a₁+14d=140    (2)

With the equiations (1) and (2)  build a system of equations
a₁+11d=41
a₁+14d=140

we solve it.
-(a₁+11d=41)
  a₁+14d=140
--------------------
       3d=99  ⇒d=99/3=33

a₁+11d=41
a₁+(11*33)=41
a₁+363=41
a₁=41-363=-322

an=a₁+(n-1)*d
an=-322+(n-1)*33
an=-322+33n-33
an=-355+33n

an=-355+33n

To check:
a₁₂=-355+33*12=-355+396=41
a₁₅=-355+33*15=-355+495=140.
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