Mental Arithmetic Questions Worksheets - Level 6 Page 17
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21Sibling ages
Equations
Solve these equations.
Paul is 14 years old.
•
16 – 1 = 15, so 8k must equal 16
Show your working.
His sister is exactly 6 years younger, so this year she is 8 years
old.
•
8 x 2 = 16, so k must equal 2
8k - 1 = 15
This year, the ratio of Paul’s age to his sister’s age is 14 : 8
OR use matched
14 : 8 written as simply as possible is 7 : 4
number line
k
= ......2
When Paul is 21, what will be the ratio of Paul’s age to his
(a)
sister’s age?
m
2
+ 5 = 10
•
Ratio
5 + 5 = 10, so 2m must equal 5.
Write the ratio as
simply as possible.
Paul
:
Sister
21 (÷ 3): 15 (÷ 3)
21-6 = 15 so
•
simplifies to
2 x 2 ½ is 5, so m must equal 2 ½
Paul’s sister is 15
7
:
5
years old
(b)
When his sister is 36, what will be the ratio of Paul’s age to his
m
= .......2 ½ .
sister’s age?
Write the ratio as simply as possible.
Paul
:
Sister
t
t
3
+ 4 =
+ 13
Partition 3t + 4 to make 2t + t + 4
•
?
:
36
Paul’s age is 6 more than his
This gives 2t+t+4 = t + 13
•
sister, so his age must be 42.
Remove t from both sides thus
•
42 (÷6)
: 36 (÷6)
keeping the equation balanced.
7
:
6
2t + 4 = 13
•
9 + 4 = 13, so 2t = 9
•
(c)
Could the ratio of their ages ever be 7 : 7?
•
t = 4 ½
Tick (
) Yes or No.
Yes
No
t
= .......4 ½
METHOD 1
Explain how you know.
2(3n + 7) = 8
2x4=8. This means that
METHOD 2
•
3n+7 is equal to 4 and can
Multiply everything in the
•
bracket by 2. This gives
be written like this
2x3n+2x7 = 8
3n+7=4
7:7 implies that the ages will be the
-3+n=4 which means that
→ 6n+14 = 8
•
•
3n=-3 i.e. 3xn=-3
•
Subtract 14 from both
same at some point in their life. This is
sides to give 6n+14-14 = 8-
n= -1
•
true.
NOT
14
→ 6n+-6, 6xn=-6 so n = -1
•
They will never be the same age as Paul
is always six years older.
n
= ........- 1
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