Answer:
Jon is 11 years old
Step-by-step explanation:
We write the following equations describing the sentences of the problem, using the letter M to represent Jon's mom's current age, and j to represent his current age.
First sentence: "<em>Six years ago Jon was one-sixth the age of his mother</em>."
translates into:
J - 6 = (M - 6) / 6
Second sentence: "<em>in four years time his age doubled and increased
</em>
<em>by 10 will match his mother's age</em>."
2 * (J + 4) + 10 = M + 4 which removing parentheses gives: 2 J + 18 = M + 4
We solve for "M" in the first equation
6 (J - 6) = M - 6
6 J - 36 = M - 6
M = 6 J - 30
and now use this result to substitute for M in the second equation
2 J + 18 = (6 J - 30) + 4
and work on solving for J
2 J + 18 = 6 J - 30 + 4
18 + 26 = 6 J - 2 J
44 = 4 J
J = 44 / 4
J = 11
Answer:
-10, -9
Step-by-step explanation:
Let x = first negative answer
then
x+1 = second negative answer
x(x+1) = 90
x^2 + x = 90
x^2 + x - 90 = 0
(x+10)(x-9) = 0
x = (-10, 9)
Since we're looking for a negative answer, throw out the positive answer leaving:
x = -10 (first negative number)
.
Second negative number"
x+1 = -10+1 = -9
Each pencil should be sold for 6
6*20 = 120 which is a 20 profit
