A bakery packages two types of gift baskets containing gourmet croissants and blueberry mu… — GRE General Test

A bakery packages two types of gift baskets containing gourmet croissants and blueberry muffins. Basket X contains $4$ croissants and $3$ muffins, with a total production cost of $\$19.00$ . Basket Y contains $2$ croissants and $5$ muffins, with a total production cost of $\$16.50$ . Assuming the cost per croissant and the cost per muffin are constant across all baskets, what is the production cost, in dollars, of a single croissant?

Cevap: 3.25 dollars

Cevap

The production cost of a single croissant is 3.25 dollars.

Let

c

represent the cost of a croissant and

m

represent the cost of a muffin. The given situation translates to the system of equations

4c + 3m = 19.00

and

2c + 5m = 16.50

. Multiplying the second equation by

2

gives

4c + 10m = 33.00

. Subtracting

4c + 3m = 19.00

from

4c + 10m = 33.00

results in

7m = 14.00

, which gives

m = 2.00

. Substituting

m = 2.00

into

2c + 5(2.00) = 16.50

yields

2c + 10 = 16.50

, so

2c = 6.50

and

c = 3.25

. Thus, a single croissant costs $3.25 dollars.

Adım Adım Çözüm

Set up a system of linear equations

4c + 3m = 19.00

and

2c + 5m = 16.50

Translate the contents and costs of Basket X and Basket Y into algebraic equations where

c

is the price of a croissant and

m

is the price of a muffin.

Eliminate variable c

4c + 10m = 33.00

, then subtracting

4c + 3m = 19.00

yields

7m = 14.00

, so

m = 2.00

Multiplying the second equation by 2 aligns the coefficients of

c

, allowing elimination by subtraction.

Solve for variable c

2c + 5(2.00) = 16.50 \implies 2c = 6.50 \implies c = 3.25

Substitute the value found for

m

back into one of the original linear equations to calculate the cost of a croissant.

Anahtar Kavram

Solving Systems of Linear Equations via Elimination

Alternatif Yöntem

Express

c

in terms of

m

using the second equation:

c = 8.25 - 2.5m

. Substitute this expression into the first equation:

4(8.25 - 2.5m) + 3m = 19.00 \implies 33 - 10m + 3m = 19.00 \implies -7m = -14.00 \implies m = 2.00

. Finally, calculate

c = 8.25 - 2.5(2.00) = 3.25

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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Alternatif Yöntem

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