A coffee shop sells two sizes of bagged coffee: a standard bag and a deluxe bag. On Monday… — SAT

A coffee shop sells two sizes of bagged coffee: a standard bag and a deluxe bag. On Monday, the shop sold $8$ standard bags and $5$ deluxe bags for a total of $\$108$ . On Tuesday, the shop sold $6$ standard bags and $10$ deluxe bags for a total of $\$156$ . What is the price, in dollars, of one deluxe bag of coffee?

Answer: 12 dollars

Answer

The price of one deluxe bag of coffee is

12

dollars.

By setting up a system of equations, we represent the total cost on Monday as

8s + 5d = 108

and on Tuesday as

6s + 10d = 156

. Multiplying the first equation by

2

gives

16s + 10d = 216

. Subtracting the second equation yields

10s = 60

, so

s = 6

. Substituting

s = 6

into the first equation yields

8(6) + 5d = 108

, which simplifies to

48 + 5d = 108

, then

5d = 60

, and finally

d = 12

Step-by-Step Solution

Define the variables and write the system of equations.

Let

s

be the price of a standard bag and

d

be the price of a deluxe bag. The system is:

8s + 5d = 108

6s + 10d = 156

To translate the word problem into mathematical equations.

Multiply the first equation by

2

to align the coefficients of

d

16s + 10d = 216

To prepare for elimination of the variable

d

Subtract the second equation from the new equation to solve for

s

10s = 60

, which simplifies to

s = 6

To eliminate

d

and find the price of a standard bag.

Substitute the value of

s

back into one of the original equations to solve for

d

8(6) + 5d = 108 \implies 48 + 5d = 108 \implies 5d = 60 \implies d = 12

To find the price of a deluxe bag.

Key Concept

Solving systems of linear equations using the elimination method.

Estimated Time:1m 30s

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