SOLUTION: The Everton College store paid $1930 for an order of 49 calculators. The store paid $10 for each scientific calculator. The others, all graphing calculators, cost the store $55 eac
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Question 464083: The Everton College store paid $1930 for an order of 49 calculators. The store paid $10 for each scientific calculator. The others, all graphing calculators, cost the store $55 each. How many of each type of calculator was ordered?
The store ordered______scientific calculators and _______graphing calculators. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! total for all calculators was equal to 1930 dollars.
there were 49 calculator total.
each scientific calculator cost 10 dollars.
each of the other types of calculator cost 55 dollars.
let x = number of scientific calculators.
let y = number of other calculators.
your formula is:
10*x + 55*y = 1930
x + y = 49
this is 2 equations that need to be solved simultaneously, meaning that the same value of x and the same value of y needs to be able to satisfy the conditions of both equations.
solve for y in the second equation to get y = 49 - x.
use that value of y in the first equation to get 10*x + 55*(49-x) = 1930.
simplify this to get 10*x + 55*49 - 55*x = 1930.
simplify further to get -45*x + 2695 = 1930.
subtract 2695 from both sides of the equation to get -45*x = -765
divide both sides by -45 to get x = 17
use that value of x in the first equation to get 10*(17) + 55*y = 1930.
simplify to get 170 + 55*y = 1930.
subtract 170 from both sides of the equation to get 55*y = 1760
divide both sides of the equation by 55 to get y = 32.
x = 17 and y = 32.
x + y becomes 17 + 32 which equals 49 satisfying the requirements of the second equation.
10*x + 55*y becomes 10*17 + 55*32 becomes 170 + 1760 which equals 1930 satisfying the requirements of the first equation.
this confirms your answer is good.
the answer is:
x = 17 which means that the number of scientific calculators is equal to 17.
y = 32 which means that the number of other calculators is equal to 32.
