Jane will receive 18% less of her regular pay when she retires. Her regular pay is $500 per week.
a How much would she receive per week if she retires today?
answer: 500/18% = 90 500-90= $410
b. Explain how you can make this same calculation using 100%-18%=82%
answer: same as above
c. show why these calculations are equivalent in general. (Hint: Write an expression for finding an amount A minus n% of A. Write another expression for finding (100-n)% of A and then use algebra to show that these two expressions are the same.)
Don't know the answer for this one.
Use n instead of 18% in your first and second calculations.
a.
500*n%=5n
net receipt=500-5n = 500(1-n/100)
b.
100%-n%=(100-n)%
net receipt = 500(100-n)% = 500(1-n/100)
Since a and b are the same, so the two calculations are equivalent for any value of n.
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what is the expression for finding an amount a minus n% of a write another expression for finding (100-n)% of a and then use algebra to show that these two expression are the same
c. To show that the calculations from parts a and b are equivalent, let's use algebra.
First, let A represent the regular pay amount of $500.
In part a, we deducted 18% from A and received $410.
To express this mathematically, we can write:
A - 18% of A = 410
Now, let's simplify the expression by converting 18% to its decimal form (0.18):
A - 0.18A = 410
Combining like terms, we have:
(1 - 0.18)A = 410
Simplifying further, we find:
0.82A = 410
Next, divide both sides by 0.82 to solve for A:
A = 410 รท 0.82
Simplifying the right side:
A = 500
As we can see, the original amount A equals $500, which is the regular pay amount we started with. Thus, we have shown that the calculations are equivalent.
In part b, we used a different approach by calculating 82% of the regular pay amount A, which is also equivalent to 100% minus 18% of A.
Therefore, the calculations in parts a and b are equivalent and will yield the same result.