Answer to Question #112204 in Algebra for kelly

Question

A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized that she didn't order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measuring tape and paid $178.90. How much does one calculator cost? How much does one measuring tape cost?

Answer 1

Let $x$ be a price of one calculator and $y$ be a price of one measuring tape.

A teacher paid $495 for 20 calculators and 10 measuring tapes

$$20x+10y=495$$

A teacher paid $178.90 for 8 calculators and 1 measuring tape

$$8x+y=178.90$$

$$2x+y=49.50$$ $$8x+y=178.90$$

$$6x=129.40$$ $$y=49.50-2x$$

$$x={64.70 \over 3}$$ $$y=49.50-2x$$

$\dfrac{64,70}{3}$ is not integer. I think the condition is wrong.

She placed another order of 8 of the same calculators and 1 more of the same measuring tape and paid $178.50.

$$20x+10y=495$$ $$8x+y=178.50$$

$$2x+y=49.50$$ $$8x+y=178.50$$

$$6x=129$$ $$y=49.50-2x$$

$$x=21.50$$ $$y=6.50$$

One measuring tape costs $6.50