The number of days Super Sally and Lazy Petunia work are illustrations of simultaneous equations
(a) Super Sally and Lazy Petunia
Represent their earnings with the first letters.
So, we have:
[tex]\mathbf{L = \frac 12S}[/tex] -- number of days
[tex]\mathbf{20L + 57S= 7733}[/tex] --- the total earnings
Make S the subject in [tex]\mathbf{L = \frac 12S}[/tex]
[tex]\mathbf{S = 2L}[/tex]
Substitute 2L for S in [tex]\mathbf{20L + 57S = 7733}[/tex]
[tex]\mathbf{20L + 57 \times 2L = 7733}[/tex]
Expand
[tex]\mathbf{20L + 114L = 7733}[/tex]
Add
[tex]\mathbf{134L = 7733}[/tex]
Divide both sides by 134
[tex]\mathbf{L = 57.7}[/tex]
From the options, the closest to 57.7 is 60.
Hence, the number of days that Petunia worked is closest is 60
(b) 4 digit even numbers
The digits are given as: 0, 1, 5, 6, 7, 8 and 9
To create a 4-digit number, the first digit cannot be 0.
So, the first digit can be any of the remaining 6
Because, it is an even number, the number can only end with 0, 6 or 8
So, the last digit can be any of the 3
Since there is no repetition, the second and the third digits can be any of the remaining 5 and 4 digits, respectively.
So, the number of digits is:
[tex]\mathbf{n =6 \times 3 \times 5 \times 4}[/tex]
[tex]\mathbf{n =360}[/tex]
Hence, the number of digits is (d) 360
(c) The value of 28^983 x 98^984/14^2948
Rewrite the expression as:
[tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex]
Express all number as a base of 14
[tex]\mathbf{\frac{14^{2 \times 983} \times 14^{7 \times 984}}{14^{2948}} }[/tex]
Apply law of indices
[tex]\mathbf{14^{2 \times 983+7 \times 984-2948}}[/tex]
Evaluate all products
[tex]\mathbf{14^{1966+6888-2948}}[/tex]
Evaluate the exponent
[tex]\mathbf{14^{5906}}[/tex]
Hence, the result of [tex]\mathbf{\frac{28^{983} \times 98^{984}}{14^{2948}}}[/tex] is [tex]\mathbf{14^{5906}}[/tex]
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