Question

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a one loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?

Answer 1

The combined cost of one loaf of bread and one package of cheese is $\boxed{\ 6.5}.$

Further explanation:

Explanation:

Consider the cost of one loaf of bread as $x.$

Consider the cost of one package of cheese as $y.$

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $\ 27.$

$\begin{aligned}6x + 3y &= 27\\\frac{{6x}}{3} + \frac{{3y}}{3} &= \frac{{27}}{3}\\2x + y &= 9\\y + 2x &= 9\\\end{aligned}$

The cost of a package of cheese is $\ 1.50$ more than the cost of a one loaf of bread.

$y = 1.5 + x$

Substitute $1.5 + x$ for y in equation $y + 2x = 9.$

$\begin{aligned}1.5 + x + 2x &= 9\\1.5 + 3x &= 9\\3x &= 9 - 1.5\\3x &= 7.5 \\ x &= \frac{{7.5}}{3} \\ x &= 2.5\\\end{aligned}$

The cost of one package of cheese can be obtained as follows,

$\begin{aligned}y&= 1.5 + 2.5\\&= 4\\\end{aligned}$

The combined cost of one loaf of bread and one package of cheese can be obtained as follows,

$\begin{aligned}x + y &= 2.5 + 4\\&= 6.5\\\end{aligned}$

The combined cost of one loaf of bread and one package of cheese is $\boxed{\ 6.5}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: Mason, 6, loaves, bread, packages, cheese, total, $27, loaf, combined, cost, bought, $1.50, loaves of bread, packages of cheese, combined cost, one loaf of bread, one package of cheese, cheese is $1.50 more.

Answer 2

Answer:

The combined cost of one loaf of bread and one package of cheese is $6.5

Step-by-step explanation:

Given :

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27.

The cost of a package of cheese is $1.50 more than the cost of a one loaf of bread.

To Find :The combined cost of one loaf of bread and one package of cheese.

Solution :

Let cost of one loaf of bread is $x.

Cost of 6 loaves of bread = $6x.

Let cost of one package of cheese is $y.

Cost of 3 packages of cheese = $3y.

Since we are given that combined cost of 6 loaves of bread and 3 packages of cheese is $27.

⇒ 6x + 3y = 27  ----(A)

We are also given that the cost of a package of cheese is $1.50 more than the cost of a one loaf of bread.

⇒y = x + 1.50 ----(B)

Solving (A) and (B) using substitution method

Substitute value of y from (B) in (A)

⇒6x + 3(x + 1.50 ) = 27

⇒6x +3x +4.5 = 27

⇒9x + 4.5 = 27

⇒9x = 27-4.5

⇒9x = 22.5

⇒x = 22.5/9

⇒x = 2.5

Thus, The cost of one loaf of bread 'x' = $2.5

Substitute this value of x in (B) to get cost of one package of cheese 'y'

⇒y =2.5 + 1.50

⇒ y = 4

Thus, The cost of one package of cheese 'y' = $4

Thus the combined cost of one loaf of bread and one package of cheese i.e. x + y = $2.5+$4 =$6.5

Hence , The combined cost of one loaf of bread and one package of cheese is $6.5