Question 654507
a restaurant manager bought 80 lb of hamburger and 30 lb of steak for a total
 cost of 163 a second purchase at the same prices includes 150 lb of hamburger
 and 50 lb of steak and costs 290 find price of 1 lb of hamburger
:
let h = cost per pound for hamburger
let s = cost per pound for steak
:
Write a total cost equation for each order
80h + 30s = 163
150h + 50s = 290
:
We are going to us elimination; mult the 1st eq by 5, the 2nd eq by 3, results:
400h + 150s = 815
450h + 150s = 870
------------------subtraction eliminates s, find h
-50h + 0 = -55
h = -55/-50
h = $1.10 a pound for hamburger
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a coin bank contains only dimes and quarters the total value is 3.70.
 if the dimes were quarters and the quarters were dimes the total value
 would be 2.95 find the number of quarters
:
Let x = original number of dimes
Let y = original number of quarters
:
Write an equation for each scenario
.10x + .25y = 3.70
.25x + .10y = 2.95
:
Using elimination again, mult the 1st equation by 5, the 2nd eq by 2
.50x + 1.25y = 18.50
.50x + .20y = 5.90
-------------------subtraction eliminates x, find y (quarters)
0 + 1.05y = 12.60
y = 12.6/1.05
y = 12 quarters
:
You should check both these problems by finding the other variable value.
Then substitute the values in the original equations, to see if it is true.