A bakery sells blueberry muffins and bran muffins. The total cost of 6 blueberry muffins a… — SAT

A bakery sells blueberry muffins and bran muffins. The total cost of $6$ blueberry muffins and $4$ bran muffins is $\$22.00$ . The total cost of $5$ blueberry muffins and $8$ bran muffins is $\$26.50$ . What is the cost, in dollars, of $1$ blueberry muffin?

Cevap: 2.5 dollars

Cevap

The cost of one blueberry muffin is 2.5 dollars.

The correct answer is 2.5. By setting up the system of linear equations

6x + 4y = 22

and

5x + 8y = 26.5

, where

x

represents the cost of one blueberry muffin and

y

represents the cost of one bran muffin, we can solve for

x

. Multiplying the first equation by 2 gives

12x + 8y = 44

. Subtracting the second equation,

5x + 8y = 26.5

, from the modified first equation yields

7x = 17.5

. Dividing by 7 results in

x = 2.5

Adım Adım Çözüm

Set up a system of equations.

6x + 4y = 22

and

5x + 8y = 26.5

Translate the context into mathematical statements where

x

is the price of a blueberry muffin and

y

is the price of a bran muffin.

Multiply the first equation by 2.

12x + 8y = 44

Align the coefficients of

y

to facilitate elimination.

Subtract the second equation from the modified first equation.

7x = 17.5

Eliminate the variable

y

to solve for

x

Divide by 7.

x = 2.5

Isolate the variable

x

to find the cost of a blueberry muffin.

Anahtar Kavram

Solving systems of two linear equations using elimination.

Alternatif Yöntem

Alternatively, solve for

y

in terms of

x

using the first equation:

y = 5.5 - 1.5x

. Substitute this expression into the second equation:

5x + 8(5.5 - 1.5x) = 26.5

, which simplifies to

5x + 44 - 12x = 26.5 \\Rightarrow -7x = -17.5 \\Rightarrow x = 2.5

Tahmini Süre:1m 30s

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