Answer:
y=2
Step-by-step explanation:
First, you substitute x with 2.
3(2)-6y=(-6)
Then, you multiply:
6-6y=(-6)
Next, you subtract 6 from -6. So, the first 6 gets crossed out because of inverse of operation.
-6y=-12
Finally, you divide -6 to both sides of the equation to get y=2
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
Answer:
Dasha has 52 roses
Step-by-step explanation:
Rewrite the first sentence in an equation: (D= Dasha) (A= Anna)
D=4A
Rewrite the second sentence in an equation:
A+39=D
1) Substitute A+39 as D in the first equation:
A+39=4A
2) Subtract A from both sides:
3A=39
3) Divide both sides by 3:
A=13
4) Now substitute 13 as A in the second equation:
13+39=D
5) Solve:
D=52
.75x+4=.75
hope this helps!
