I need to find out the equations for these problems

A puppy pen is 1 foot longer than twice its width. John wants to increase the length and width by 5 feet each to enlarge the area by 90 square feet. What will be the area of the new pen?

Keesha has 10 more quarters than dimes, which, together, total $11.25. How many coins does she have in quarters and dimes?

I need the equations, because i have to solve by graphing, so help please?

let x be the length and y be the width
A puppy pen is 1 foot longer than twice its width means
x = 2*y +1
The area of the pen is x*y, substitute x = 2*y+1 in this
A = (2*y + 1)*y = 2*y^2 + y

When John increases the length and width by 5 feet each, the new area will be
Anew = (2*y + 1 + 5)*(y+5) = 2*y^2 + 10*y + 6*y + 30 = 2*y^2 + 16*y + 30

And this enlarges the area by 90 squarefeet. So the difference between two areas must be 90
Anew - A = (2*y^2 + 16*y + 30) - (2*y^2 + y) = 15*y + 30 = 90
now you can solve for y and then solve x
y = (90-30)/15 = 4 feet
x = 2*y+1 = 2*4+1 = 9 feet

let q be the number of quarters and d be the number of dimes
q = d + 10
0.25*q + 0.1*d = 11.25 (because each q is worth 0.25 and each d is worth 0.10)

plug q = d + 10 in the second equation and solve for d
0.25*(d + 10) + 0.1*d = 11.25
0.25*d + 2.5 + 0.1*d = 11.25
0.35*d = 8.75
d = 8.75/0.35 = 25

plug this in the first equation and solve for q
q = d + 10 = 35

You can graph a straight line by taking two points from that equation and connecting those points. You already have one point: (9, 4) the solution to the problem. Take another arbitrary y value (say y=8), solve for x (x=2*y+1=2*8+1=17), so you have (17,8). Mark these points and connect them

Report Abuse