The Everton college store paid $1859 for an order of 49 calculators. The store paid $11 each for scietific calculators. The others, all graphing calculators, cost the store $55 eaach. How many of each type of calculator ws ordered? Please answer in detail so that I can see what is wrong and where. thank you.
Let we have S scientific and G graphing
calculators. Then
S+G=49
11S+55G=1859
S=49-G
11(49-G)+55G=1859
S=49-G
44G=1859-539
G=30
S=19
To solve this problem, we can use a system of equations. Let's represent the number of scientific calculators as "x" and the number of graphing calculators as "y".
From the given information, we can set up two equations:
Equation 1: x + y = 49 (since the total number of calculators ordered is 49)
Equation 2: 11x + 55y = 1859 (since the total cost of the order is $1859)
Now, we can solve this system of equations to find the values of x and y.
Begin by solving Equation 1 for x:
x = 49 - y
Next, substitute the value of x in Equation 2:
11(49 - y) + 55y = 1859
Distribute:
539 - 11y + 55y = 1859
Combine like terms:
44y = 1320
Divide both sides by 44:
y = 30
Now that we have the value of y, substitute it back into Equation 1 to find x:
x = 49 - 30
x = 19
Therefore, 19 scientific calculators and 30 graphing calculators were ordered.
To double-check if the solution is correct, we can verify the cost:
11(19) + 55(30) = 209 + 1650 = 1859
The total cost matches the given value, so the solution is correct.
If you encountered any mistakes, I recommend checking your calculations or ensuring you set up the equations correctly.