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Question 476442: Assign x and y for unknown values, create system of two equations and find solution:
Simple calculator costs $5 and scientific calculator costs $16.
The store sold 35 calculators and received $340.
How many of each calculator was sold?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let X equal the number of simple $5 calculators sold. Let y equal the number of scientific $16 calculators sold.
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If you add together these two numbers, the total must be 35 because that is the total number of calculators sold.
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So one equation that you know is:
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x + y = 35
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If x of the simple calculators were sold and the cost of each was $5, then the total amount of money obtained for these calculators was 5*x dollars. Similarly, if y was the number of scientific calculators sold, then the amount of money obtained for these scientific calculators was 16*y dollars. Adding these two amounts together results in the total amount of $340 for selling calculators. In equation form this gives you the second equation of:
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5x + 16y = 340
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You have two unknowns (x and y) and two independent equations. The problem can now be solved. There are a number of ways to solve this. One of them is by substitution. You can solve the first equation for x in terms of y and then substitute that value into the second equation. So start with the first equation:
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x + y = 35
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Subtract y from both sides of the equation:
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x = 35 - y
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Now substitute the right side of this equation for x in the second equation:
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5x + 16y = 340
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5(35 - y) + 16y = 340
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Do the distributed multiplication [5 times the numbers in parentheses] and the equation becomes:
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175 - 5y + 16y = 340
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Subtract 175 from both sides of this equation to get rid of it on the left side:
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- 5y + 16y = 340 - 175
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Combine the y terms on the left side:
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+ 11y = 340 - 175
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And combine the number terms on the right side:
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+11y = 165
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Solve for y by dividing both sides by 11 to get:
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y = 15
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So we now know that 15 scientific calculators were sold. And since we know that the total number of calculators sold was 35, we can subtract 15 from 35 to get the answer that 20 simple calculators were sold.
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You can check this by multiplying the 20 simple calculators times $5 to find that $100 was collected from the sale of simple calculators. And then multiply the 15 scientific calculators times the $16 cost for each. That multiplication results in $240 for scientific calculators. Adding together the two amounts results in:
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$100 + $240 = $340
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And that is just the amount it should be according to the problem. So the answers are correct:
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15 scientific calculators were sold and 20 simple calculators were sold.
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Hope this helps you to understand this problem a little better.
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