Question

A mign school math department purchased brand A calculators for $80 each and brand B calculators for $95 each. It purchased a total of 20 calculators at a total cost of $1780. How many brand A calculators did the department purchase?

Answer 1

SEE BELOW⬇

Explanation:

Let A represent the number of brand A calculators purchased, and B represent the number of brand B calculators purchased.

We have two pieces of information:

• The cost of each brand A calculator is $80, and the cost of each brand B calculator is $95.
• The total cost of all calculators is $1780.

We can write two equations based on this information:

• 80A + 95B = 1780 (total cost equation)
• A + B = 20 (total number of calculators equation)

↪ Now, we can solve this system of equations. Let's use the second equation (A + B = 20) to express one of the variables in terms of the other. Let's solve for A:

• A = 20 - B

Now, substitute this expression for A into the first equation (80A + 95B = 1780):

• 80(20 - B) + 95B = 1780

Now, distribute 80:

• 1600 - 80B + 95B = 1780

Combine like terms:

• 15B = 1780 - 1600

• 15B = 180

Now, divide by 15 to find B:

• B = 180 / 15 = 12

So, the department purchased 12 brand B calculators.

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➡ To find the number of brand A calculators, use the equation A = 20 - B:

• A = 20 - 12 = 8

∴ department purchased 8 brand A calculators.