ALGEBRAIC TRANSLATION PROBLEM

Question

Hello,

Having some trouble understanding the math behind this problem. The translation part was no problem, but why combine the two equations by subtracting equation 1 from equation 2?

"Cableb spends $72.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?"

I translated:
a = single
b = double

1a + 1.5b = 72.50
a + b = 50

Thanks in advance.

fluke · Answer

a+1.5b=72.5

Multiplying the equations by 2;
2a+3b=145----------1
2a+2b=100----------2

Subtract 2 from 1:
2a+3b-2a-2b=145-100
b=45
*******************************

bunsu14 · Answer

What is the logic to combining the two equations?

fluke · Answer

Please search the net on how to solve simultaneous equations in two variable.

In short;

a+3b=5
2a+5b=20

If we have to find b; we need to cancel a.
How should be cancel a; First multiply the first equation by 2; and then subtract 1 from 2 or 2 from 1; doesn't matter

a+3b=5
Multiply by 2;
2a+6b=10

subtract;
2a+6b-2a-5b=10-20
b=-10

OR
2a+5b-2a-6b=20-10
-b=10
b=-10

bunsu14 · Answer

Thanks for taking the time out to explain, much appreciated.

Spidy001 · Answer

total amount spent on hamburgers =$72.5 ----1

let x be the single ham burgers and y be the double ham burgers

as we know the total ham burgers = 50 => x+y =50---equation 2

also as single ham burger costs $1 and double ham burger costs $1.50, we can rephrase 1 as 
 x+1.5y = 72.5 --- equation2

solving equation 2 and 3 ,

we can find out that x=5,y = 45

So the answer is 45.

toughmat · Answer

s+d = 50 -- (1)
s+1.5d = 72.5 ---(2)
we need to solve for d
(2) - (1) --> 0.5d = 22.5
d= 45

ALGEBRAIC TRANSLATION PROBLEM

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