Respuesta :
The combined cost of one loaf of bread and one package of cheese is [tex]\boxed{\$ 6.5}.[/tex]
Further explanation:
Explanation:
Consider the cost of one loaf of bread as [tex]x.[/tex]
Consider the cost of one package of cheese as [tex]y.[/tex]
Mason bought 6 loaves of bread and 3 packages of cheese for a total of [tex]\$27.[/tex]
[tex]\begin{aligned}6x + 3y &= 27\\\frac{{6x}}{3} + \frac{{3y}}{3} &= \frac{{27}}{3}\\2x + y &= 9\\y + 2x &= 9\\\end{aligned}[/tex]
The cost of a package of cheese is [tex]\$1.50[/tex] more than the cost of a one loaf of bread.
[tex]y = 1.5 + x[/tex]
Substitute [tex]1.5 + x[/tex] for y in equation [tex]y + 2x = 9.[/tex]
[tex]\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}[/tex]
The cost of one package of cheese can be obtained as follows,
[tex]\begin{aligned}y&= 1.5 + 2.5\\&= 4\\\end{aligned}[/tex]
The combined cost of one loaf of bread and one package of cheese can be obtained as follows,
[tex]\begin{aligned}x + y &= 2.5 + 4\\&= 6.5\\\end{aligned}[/tex]
The combined cost of one loaf of bread and one package of cheese is [tex]\boxed{\$ 6.5}.[/tex]
Learn more:
- Learn more about inverse of the function https://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://brainly.com/question/3412497
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.
Combined cost of one loaf of bread and one package of cheese= $6.5
Step-by-step explanation:
Given :
Total cost of 6 loaf of bread and 3 packages of cheese is $27.
The cost of a package of cheese is $1.50 more than the cost of a one loaf of bread.
Calculation :
Let the cost of one loaf of bread as x and the cost of one package of cheese as y.
Now,
[tex]6x+3y=27[/tex] ------ (1)
[tex]y=1.5+x[/tex] ----- (2)
Now solving equation (1) and (2) we get x and y,
[tex]6x + 3(x+1.5) =27[/tex]
[tex]9x+4.5=27[/tex]
[tex]x=2.5[/tex] ----- (3)
[tex]y = 4[/tex] (from equation (2) and (3))
Combined Cost = $6.5
For more information, refer to the link given below
https://brainly.com/question/13911928?referrer=searchResults
