Mary McDonald sold 11 small mugs and 10 large mugs.
Step-by-step explanation:
Given,
Total cost of sold cups = $85
Cost of one small cup = $2.50
Cost of one large cup = $5.75
Cups at the start of day = 215
Cups at the end of day = 194
Cups sold = Cups at the start of day - Cups at end of day
Cups sold = 215 - 194 = 21
Let,
x represents the number of small cups.
y represents the number of large cups.
According to given statement;
x+y=21 Eqn 1
2.50x+5.75y=85 Eqn 2
Multiplying Eqn 1 by 2.50
[tex]2.50(x+y=21)\\2.50x+2.50y=52.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](2.50x+5.75y)-(2.50x+2.50y)=85-52.50\\2.50x+5.75y-2.50x-2.50y=32.50\\3.25y=32.50[/tex]
Dividing both sides by 3.25
[tex]\frac{3.25y}{3.25}=\frac{32.50}{3.25}\\y=10[/tex]
Putting in Eqn 1
[tex]x+10=21\\x=21-10\\x=11[/tex]
Mary McDonald sold 11 small mugs and 10 large mugs.
Keywords: linear equation, subtraction
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