A little help with these few math problems!!!?

Question

1.)Mr. Charbonneau and Mr. Seward were comparing their ages. They discovered that the sum of their ages is 96. In 10 years, Mr. Charbonneau will be 14 years older than Mr. Seward is now. How old are they both today.
Be sure to use “Let” statements or a chart with the two equations.

2.)Mr. Girard is thinking of 2 numbers (he does that sometimes). He tells his class that one of the numbers is 7 less than the other. He also states that six times the smaller number is equal to 8 more than the larger number. What are the two numbers that Mr. Girard is thinking about? Be sure to use “Let” statements and two equations.

3.)A line is perpendicular to the line y= 2x + 3 and has the same x-intercept as x + 3y + 10 = 0. Find the equation of this line. Express your answer in the form y = mx + b. Justify your answer.


Please answer these math problems with math formulas and how you'd go about solving them

Answer 1

1.) Let c be Mr. Charbonneau's current age and s be Mr. Seward's current age. The sum of their ages is 96, so c + s = 96. In 10 years, Mr. Charbonneau will be c + 10 years old. At this time, he will be 14 years older than Mr. Seward is now, which is s years old, so c + 10 = s + 14. Solve the system of equations by elimination.



c + 10 = s + 14 (subtract s from both sides and 10 from both sides)

c - s = 4



Add this equation and the first equation c + s = 96 together to solve for c.



(c + s = 96) + (c - s = 4)

2c = 100

c = 50



Now go back to any equation to solve for s.



c + s = 96

50 + s = 96

s = 46



Mr. Charbonneau is 50 years old and Mr. Seward is 46 years old.



2.) Let x be the smaller number and y be the larger number. One number, which would be the smaller, is 7 less than the other, so x = y - 7. Also, six times the smaller number is 8 more than the larger number, so 6x = y + 8. Solve the system by substitution.



6x = y + 8 (substitute y - 7 for x)

6(y - 7) = y + 8

6y - 42 = y + 8

5y - 42 = 8

5y = 50

y = 10



x = y - 7

x = 10 - 7

x = 3



The numbers are 3 and 10.



3.) Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Perpendicular lines have slopes that are opposite reciprocals (have a product of -1). Line y = 2x + 3 has a slope of 2, so a line perpendicular to it has a slope of -1/2, thus its equation so far in slope-intercept form is y = (-1/2)x + b. This line also has the same x-intercept as x + 3y + 10 = 0. Solve for the x-intercept, which is when y = 0.



x + 3y + 10 = 0

x + 3(0) + 10 = 0

x + 10 = 0

x = -10



The x-intercept is point (-10, 0). Substitute this point into the equation y = (-1/2)x + b for x and y respectively to solve for b.



y = (-1/2)x + b

0 = (-1/2)(-10) + b

0 = 5 + b

-5 = b



The equation of the line is y = (-1/2)x - 5.

Answer 2

1:



X1 + X2 = 96

X1 + 10 = X2 + 14



You have a system of 2 equations and 2 unknowns. Solve one equation for a variable in terms of the other, then substitute that into the 2nd equation. IE: X1 = 96 - X2, Substitute 96 - X2 for X1 in the other equation, yielding 96 - X2 + 10 = X2 + 14. Solve for the variables. X2 = 46, X1 = 50.



2:



X1 - 7 = X2

6 * X2 = X1 + 8



X1 = X2 + 7 => 6 * X2 = (X2 + 7) + 8 => X2 = 3. Therefore X1 = 10.



3:



I made a typo and I see someone else has submitted it anyway.



This is really, really, really basic algebra, so assuming you're in middle school, you should've reasonably been able to do these, you just needed to actually read the questions and convert the words into numbers. There's no tricks involved.

Answer 3

enable x signify the fee of the completed quarters. x+ 2x + x+2 = $7.60 4x = 7.60 - 2 4x = 5.60 x = a million.40 ( fee of quarters) 2x = $2.80 ( fee of dimes ( fee of nickels) = 7.60 - (a million.40 + 2.80) = $3.40 What confuses me is : why would not x+2 ( nickels) = $3.40 ???