the everton college store paid $1553 for an order of 42 calculators. the store paid $9 for each scientific calculator. the others, all graphing calculators, cost the store $56 each. how many of each trupe of calculator was ordered?
the store ordered:
how many scientfic calculators?
graphing calculators?
Let
S = number of scientific calculators
"an order of 42 calculators."
42-S = number of graphing calculators.
"the store paid $9 for each scientific calculator... graphing calculators, cost the store $56 each"
Total cost
= $9*S + $56*(42-S)
Since the total cost is $1553, solve for S in
$1553 = $9*S + $56*(42-S)
To find out how many scientific calculators and graphing calculators were ordered by the Everton College store, we can set up a system of equations.
Let's represent the number of scientific calculators as "x" and the number of graphing calculators as "y."
We know that the store ordered a total of 42 calculators, so we can write our first equation as:
x + y = 42 (equation 1)
We also know that the store paid $9 for each scientific calculator, so the total cost of the scientific calculators is 9x.
The store paid $56 for each graphing calculator, so the total cost of the graphing calculators is 56y.
The store's total cost for the order is $1553, so we can write our second equation as:
9x + 56y = 1553 (equation 2)
Now, we can solve the system of equations (equations 1 and 2) to find the values of x and y.
To make the process easier, we can use the substitution method:
1. Solve equation 1 for x:
x = 42 - y
2. Substitute this value of x into equation 2:
9(42 - y) + 56y = 1553
Simplifying:
378 - 9y + 56y = 1553
Combine like terms:
47y = 1175
Divide both sides by 47:
y = 25
3. Substitute the value of y back into equation 1 to solve for x:
x = 42 - 25
x = 17
Therefore, the store ordered 17 scientific calculators and 25 graphing calculators.