Question

7. If the age of a father is 6 times the age of his son and the total age of the father and his
son is 42, find their ages.
Solution
8. There are only two kinds of fruit for sale, apple and orange. The prices of an apple
and an orange are $4 and $5 respectively. On a certain day, the number of apples
sold is 6 times the number of oranges sold and the sum of money for the fruit sold is
$1 479. Find the total number of fruit sold that day. HKDSE reference 17 Paper 1
Solution

Answer 1

7. The son's age is 6 and his father's is 36.

Let the age of the son be $x$ and the age of his father be $y$,

$x+y=42\\6x=y$

substitute $6x$ for $y$ in $x+y=42$ to find the age of the son:

$x+y=42\\x+6x=42\\7x=42\\x=6$

since $6x=y$, substitute the value of $x =6$ to find the age of the father:

$6x=y\\x=6\\y=6*6\\y=36$

8. The total number of fruit sold is 304.

Let oranges be $x$ and apples be $y$,

$4x+5y=1479\\y=6x$

substitute $6x$ to find the number of oranges:

$4x+5y=1479\\4x+5(6x)=1479\\4x+30x=1479\\34x=1479\\x=43.5$

now solve for $y$ to find the number of apples:

$y=6x\\y=6*43.5\\y=261$

add the two together to find the total number of fruit:

$x+y = 43.5+261=304.5$ ≈ $304$ (rounded up because fruit count is a whole number)