SOLUTION: In New York, the verrazano bridge charges a toll of $15. Thr Bronx-Whitestone bridge.charges $7.50. Suppose you use each.bridge some number of times, for a total of 11 uses. If you

Question 1086082: In New York, the verrazano bridge charges a toll of $15. Thr Bronx-Whitestone bridge.charges $7.50. Suppose you use each.bridge some number of times, for a total of 11 uses. If you spend 105 in total on tolls, how many times did you use each bridge?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = number of times the Verrazano bridge is crossed
y = number of times the Bronx-Whitestone bridge is crossed
x and y are positive whole numbers

They must add to 11 because we're told "you use each bridge...for a total of 11 uses"
x+y = 11

Solve for y to get
x+y = 11
x+y-x = 11-x
y = 11-x
We'll use this equation later

It costs $15 to cross the Verrazano bridge. If you cross it x times, then you spend 15*x dollars for this bridge alone.

It costs $7.50 to cross the Bronx-Whitestone bridge. If you cross this bridge y times, then it costs 7.50*y dollars just for this bridge alone

In total, it will cost you 15*x + 7.50*y dollars for both bridges combined. This total is equal to $105.

So we have this equation
15*x + 7.50*y = 105

Replace y with 11-x. This works because y = 11-x is the equation we found earlier
15*x + 7.50*y = 105
15*x + 7.50*( y ) = 105
15*x + 7.50*( 11-x ) = 105

Now solve for x
15*x + 7.50*( 11-x ) = 105
15*x + 7.50*( 11 ) + 7.50*( -x ) = 105
15*x + 82.5 - 7.50*x = 105
7.5*x + 82.5 = 105
7.5*x + 82.5 - 82.5 = 105 - 82.5
7.5*x = 22.5
7.5*x/7.5 = 22.5/7.5
x = 3

You used the Verrazano bridge 3 times

Use x = 3 to find y
y = 11-x
y = 11-3
y = 8

You used the Bronx-Whitestone bridge 8 times

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