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 t

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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 t

he cost of a one loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?

Mathematics

2 answers:

PIT_PIT [3.9K] · Answer 1 · 2026-02-19T22:57:22+03:00

The total cost for one loaf of bread plus one cheese package is $\boxed{\$ 6.5}.$

Further explanation:

Explanation:

Assume the price of one loaf of bread is $x.$

Assume the price of one cheese package is $y.$

Mason purchased 6 loaves and 3 cheese packages paying 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 cheese package costs $\$1.50$ more than a loaf of bread.

$y = 1.5 + x$

Replace $1.5 + x$ with y in the 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 cheese package is determined as follows,

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

The combined cost of a loaf plus a cheese package is calculated as,

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

The total price for one loaf of bread and one cheese package is $\boxed{\$ 6.5}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equations

Keywords: Mason, 6 loaves bread, packages cheese, total $27, loaf, combined cost, bought, $1.50 price difference, package cheese more, single loaf, single package cheese.

Svet_ta [4.3K] · Answer 2 · 2026-02-19T22:57:01+03:00

Answer:

The total price for one loaf of bread combined with one package of cheese is $6.5.

Step-by-step explanation:

Given:

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

The price of one cheese package exceeds the price of one loaf of bread by $1.50.

To find: The sum cost of a single loaf of bread plus one cheese package.

Solution:

Let the price per loaf of bread be $x.

The cost for 6 loaves is $6x.

Let the price per cheese package be $y.

The cost for 3 cheese packages is $3y.

We know the total for both is $27:

6x + 3y = 27 ----(A)

Also, the cheese package costs $1.50 more than a loaf of bread:

y = x + 1.50 ----(B)

Using substitution, plug (B) into (A):

6x + 3(x + 1.50) = 27

6x + 3x + 4.5 = 27

9x + 4.5 = 27

9x = 22.5

x = 2.5

Therefore, the price of one loaf of bread is $2.5.

Now substitute $2.5 for x in (B):

y = 2.5 + 1.50 = 4

So, one cheese package costs $4.

Hence, the combined price is $2.5 + $4 = $6.5

Therefore, the combined cost of one loaf of bread and one package of cheese equals $6.5.