A store sells two sizes of mugs: a small mug for $3.50 and a large mug for $6.80. A guy buys 15 mugs and pays $69. How many of each size does he buy?

Question

Please answer ASAP!!!

Answer 1

Hi Jeremy

 

let x be the number of small mugs he buys. Let y be the number of large mugs he buys.

 

We know that x+y =15 (the total number of mugs he buys)

 

We also know the prices of the mugs.  So, we can reason that the total price (69) = 3.50x + 6.80y

 

Use the first equation to solve for x. 

 

x = 15 - y

 

Now you can plug that value of x into the other equation.

 

69 = 3.50(15 - y ) + 6.80y

 

Now, solve for y.

 

69 = 52.5 -3.50y + 6.80y

69= 52.5 + 3.3y

16.5 = 3.3y

y = 5

 

so, we know the man bought 5 large mugs. You can plug that value for y back into x+y=15

 

x+5=15

x+10

 

So, the man bought 10 small mugs and 5 large ones!

 

 

 

 

Answer 2

Hello Jeremy,

Thank you for posting the question!  We are looking for two unknowns, and we are given two pieces of information about the unknowns.

(1) How many mugs we have in total, and (2) Total Sale Amount for the total # of mugs.

 

That is, if we let

S = # of small mugs, and L = # of large mugs, we have

 

(1)    S + L = 15 and

(2)    3.5(S) + 6.8(L) = 69

 

To use 'Elimination Method', multiply Equation (1) by -3.5, yielding

(2)    3.5(S) +  6.8(L) = 69

(3)   -3.5(S) -  3.5(L) = -52.5

 

Adding the two equations together yields:

 

(4)    3.3(L) = 16.5

 

Divide both sides by 3.3 to get:

 

(5)     L = 5

 

Plugging this back into Equation (1) yields:

 

(6)     S=10

 

Hope that helps.  If you have any further questions on it, happy to to hear from you.

Best Regards,

Michael