Answer:
115
Step-by-step explanation:
20% is one fifth. If Mary has one fifth fewer than Susan, then she has 4 fifths of what Susan has. So 92 is 4 fifths of some number.
To find out what one fifth is, you can divide 92 by 4 because it is four fifths.
92/4 = 23
So one fifth of the number of blouses Susan has is 23. Now you can multiply 23 by 5 to get the total number of blouses Susan has.
23 * 5 = 115
Let <em>n</em> be the unknown number. We can write it as
<em>n</em> = 10<em>a</em> + <em>b</em>
with <em>a</em> and <em>b</em> integers between 1 and 9 (either with positive or negative sign).
Reversing the digits gives another number
<em>m</em> = 10<em>b</em> + <em>a</em>
The first number is increased by 54 when the digits are reversed, which means
<em>m</em> = <em>n</em> + 54 → 10<em>b</em> + <em>a</em> = 10<em>a</em> + <em>b</em> + 54 → 9<em>b</em> - 9<em>a</em> = 54 → <em>b</em> - <em>a</em> = 6
The digit in the tens place of <em>n</em> is 3 times the digit in the ones place, so
<em>a</em> = 3<em>b</em>
Substitute this into the previous equation and solve for <em>b</em> :
<em>b</em> - <em>a</em> = <em>b</em> - 3<em>b</em> = -2<em>b</em> = 6 → <em>b</em> = -3
Solve for <em>a</em> :
<em>a</em> = 3<em>b</em> = 3(-3) = -9
Then the original number is <em>n</em> = 10<em>a</em> + <em>b</em> = 10(-9) + (-3) = -93
Answer:
8t^3-36t^2+54t-27
Step-by-step explanation:
(2t-3)^3
(2t-3)(2t-3)(2t-3)
Multiply the first two terms
(4t^2 -6t -6t+9)(2t-3)
Combine like terms
( 4t^2 -12t +9) ( 2t-3)
Multiply
2t*( 4t^2 -12t +9) -3 ( 4t^2 -12t +9)
Distribute
8t^3 -24t^2 +18t-12t^2 +36t-27
Combine like terms
8t^3-36t^2+54t-27
Answer:
1) k = 3
2) 3, 4, 5
3) k + (k + 2) + (k + 4) = 4k
4) 6, 8, 10
Step-by-step explanation:
Jared used the equation;
k + (k + 1) + (k + 2) = 4k
Let's find k.
3k + 3 = 4k
4k - 3k = 3
k = 3
Thus,the integers will be;
3, (3 + 1) and (3 + 2)
This is; 3, 4, 5
He is looking for consecutive even integers but yet got 3 and 5 which are odd numbers. However, he should have used the format;
k, (k + 2), (k + 4) as the 3 consecutive even integers.
Thus, rewriting the main equation gives;
k + k + 2 + k + 4 = 4k
3k + 6 = 4k
4k - 3k = 6
k = 6
Thus,the integers are;
6, (6 + 2), (6 + 4)
This is; 6, 8, 10
