difficult math word problem?

Question

Frank weighs twice as much as George, but 30 pounds less than Harry. If Harry weighs 110 pounds more than George, how much does Harry weigh?

I need someone to explain this to me.. it was a part of SAT prep and I have no idea how to solve it

Answer 1

let Frank's weight be F
let George's weight be G
let Harry's weight be H

F = 2G #Eq1
F = H - 30 #Eq2
H = G + 110 #Eq3

sub Eq1 into Eq 2
2G = H - 30
G = H/2 - 15

now sub that into Eq 3
H = (H/2 - 15) + 110
2H = H - 30 + 220
H = 190

harry weighs 190 pounds

Answer 2

Let Frank = 2 * George
Harry = Frank + 30
Harry = George + 110
so
Frank + 30 = George + 110
2 * George + 30 = George + 110
subtract both sides by George to leave
George + 30 = 110
subtract 30 from both sides to give George's weight
George = 80
substitue George's weight into above problems to give Frank and Harry's weight.
Frank = 2*80 = 160
Harry = 80+110 = 190
check
Harry - Frank = 30

Answer 3

You first set up the algebra as follows:
G * 2 = F
F + 30 = H
H - 110 = G

you then plug the formulas into each other. Putting the first two together gives you:
(G*2)+30=H
This was done by replacing the F in the second formula with what was said F is equal too

Then you combine this formula with the last one as follows:
((G*2)+30)-110=G
This was done by replacing the H in the third formula with the one above.
So G=80 I just guessed and checked till i found the answer that made the equation equal.

So we use this to solve for F by pluging the first formula:
G * 2 = F
80 * 2 = F
160 = F

And we then plug the middle formula:
F + 30 = H
160 + 30 = H
190 = H

Harry weighs 190 lbs

Answer 4

set it up as multiple equations step by step.

F=2G
(2 x george's wt will = franks)

F+ 30= H
(franks wt + 30 lbs = harry)

H - 110= G
(harry's wt - 110 will = george's wt ==> remember george is heavier)
Now you're looking for H, so substitute the first exquation using F into one of the other equations so the other 2 have the same interger unknowns.

after some rearranging you can get

G- H = -110
-2G +H = 30

-G = -80 (the negatives cancel out)
G= 80 and substitute G into one of other equations to get H

H= 190

Answer 5

When you do questions like this, make sure you right down equations and use the first letters to help you out and read out the question in sections as you write equations.

Take the first part, F = 2G, F = H -30. Then there is H = G + 110. Make the first two equations equal, and solve for H. Then make the equation equal to H = G+110 . Then plug the answer for George's weight into H = G +110.

Notice that I didn't add labels for lbs; that just tends to take time but if it helps you out you'll have to weigh(no pun intended) that into your test time.
Hope that helps.

Answer 6

frank=george x 2
frank=harry - 30
Harry= George + 110

(Since frank equals two different things, you can set them equal to each other) So...

george(x)2=harry - 30

then substitute what harry is in terms of george

george(x)2= George+110-30

then subtract a george from both sides:

george = 110-30
george= 80

Now that you know geroge, you can plug him back into the problem to find harry.

80 + 110 = 190

Harry weighs 190 pounds!

There ya go.. hope I helped!!

Answer 7

if harry is 110 pounds more then george and frank is 30 pounds less than harry, then frank is 80 pounds more than george. this means that george is 80 pounds (because frank is double george. so frank is 160 pounds and Harry is 190 pounds. i hope i'm right so it helps.

Answer 8

Weights are denoted by initials of persons.

F=2G
F=H-30
H=G+110
We are interested in H so get eliminate F and G ASAP.
H-30 = 2G; G = H/2 - 15
H = G + 110 = H/2 - 15 + 110 = H/2 + 95
H/2 = 95 or H=190

Answer 9

Harry is 190
cause G=x
F=2x=H-30
H=x+110
so f=2x=x+110-30
2x=x+80
x=80
H=80+110=190

Answer 10

you minus the 30 pounds from the 110 and double the answer! thats how much frank weighs!