Question

Michael orders pizzas from Pizza by Alfredo and from Alfredo’s Pizza Cafe. The pizzas from
Pizza by Alfredo costs $3 each, and the pizzas from Alfredo’s Pizza Cafe costs $5 each. Michael spent $24 more on pizza from Alfredo’s Pizza Cafe than he did at Pizza by Alfredo. If Michael spent $66 in total, how many pizzas did he buy from each place?

Answer 1

Michael bought 7 pizzas from Pizza by Alfredo and 9 pizzas from Alfredo's Pizza Cafe.

Step-by-step explanation:

Cost of Pizza at Pizza by Alfredo = $3

Cost of pizza at Alfredo's pizza cafe = $5

Total amount spent = $66

Let,

Pizzas bought from Pizza by Alfredo = x

Pizzas bought from Alfredo's Pizza Cafe = y

According to given statement;

3x+5y=66     Eqn 1

5y = 3x+24        Eqn 2

Putting value of 5y from Eqn 2 in Eqn 1;

$3x+(3x+24)=66\\3x+3x+24=66\\6x=66-24\\6x=42$

Dividing both sides by 6

$\frac{6x}{6}=\frac{42}{6}\\x=7$

Putting x=7 in Eqn 2

$5y=3(7)+24\\5y=21+24\\5y=45$

Dividing both sides by 5

$\frac{5y}{5}=\frac{45}{5}\\y=9$

Michael bought 7 pizzas from Pizza by Alfredo and 9 pizzas from Alfredo's Pizza Cafe.

Keywords: linear equation, substitution method

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