Respuesta :
Assuming h stands for hamburgers and s stands for chicken sandwiches, then we can represent the statement like so:
[tex]4h + 7s = 34.5 \\ 8h + 12s = 30.5 [/tex]
Using Elimination method:
Multiply the first equation by 8 and multiply
the second equation by 4
[tex](8 \times 4h) + (8 \times 7s) = (8 \times 34.5) \\ (4 \times 8h) + (4 \times 3s) = (4 \times 30.5)[/tex]
Simplify
[tex]32h + 56s = 276 \\ 32h + 12s = 122[/tex]
Subtract equation 2 from 1
[tex]32h + 56s = 276 \\ - \\ 32h + 12s = 122[/tex]
[tex]44s = 154[/tex]
Simplify further by dividing both sides by the coefficient of s
[tex]s = \frac{154}{44} [/tex]
[tex]hence \: s = 3.5 \: dollars[/tex]
Substitute for s in equation 1
[tex]4h + 7(3.5) = 34.5[/tex]
[tex]4h + 24.5 = 34.5[/tex]
Collect like terms
[tex]4h = 34.5 - 24.5[/tex]
[tex]4h = 10[/tex]
[tex]h = \frac{10}{4} [/tex]
[tex]h = 2.5 \: dollars[/tex]
Hence, the cost of hamburgers is $2.5 and chicken sandwiches is $3.5
[tex]4h + 7s = 34.5 \\ 8h + 12s = 30.5 [/tex]
Using Elimination method:
Multiply the first equation by 8 and multiply
the second equation by 4
[tex](8 \times 4h) + (8 \times 7s) = (8 \times 34.5) \\ (4 \times 8h) + (4 \times 3s) = (4 \times 30.5)[/tex]
Simplify
[tex]32h + 56s = 276 \\ 32h + 12s = 122[/tex]
Subtract equation 2 from 1
[tex]32h + 56s = 276 \\ - \\ 32h + 12s = 122[/tex]
[tex]44s = 154[/tex]
Simplify further by dividing both sides by the coefficient of s
[tex]s = \frac{154}{44} [/tex]
[tex]hence \: s = 3.5 \: dollars[/tex]
Substitute for s in equation 1
[tex]4h + 7(3.5) = 34.5[/tex]
[tex]4h + 24.5 = 34.5[/tex]
Collect like terms
[tex]4h = 34.5 - 24.5[/tex]
[tex]4h = 10[/tex]
[tex]h = \frac{10}{4} [/tex]
[tex]h = 2.5 \: dollars[/tex]
Hence, the cost of hamburgers is $2.5 and chicken sandwiches is $3.5
The cost of the hamburgers is $2.5 and chicken burgers are $3.5.
Given
Two groups of people order food at a restaurant.
One group orders 4 hamburgers and 7 chicken sandwiches for $34.50.
The other group ordered 8 hamburgers and 3 chicken sandwiches for $30.50.
System of equations;
Let, the number of hamburgers is x and y the number of chicken sandwiches.
One group orders 4 hamburgers and 7 chicken sandwiches for $34.50.
[tex]\rm 4x+7y=34.50[/tex]
The other group ordered 8 hamburgers and 3 chicken sandwiches for $30.50.
[tex]\rm 8x+3y=30.50[/tex]
On solving both the equations
From equation 1
[tex]\rm 4x+7y=34.50\\\\4x=34.50-7y\\\\x = \dfrac{34.50-7y}{4}[/tex]
Substitute the value of x in equation 2
[tex]\rm 8x+3y=30.50\\\\8 (\dfrac{34.50-7y}{4}+3y=30.50\\\\2(34.50-7y)+3y=30.50\\\\ 69-14y+3y=30.50\\\\-11y=30,50-69\\\\-11y=-38.5\\\\y = \dfrac{-38.5}{-11}\\\\y=3.5[/tex]
Substitute the value of y in equation 1
[tex]\rm 4x+7y=34.50\\\\4x+7(3.5)=34.50\\\\4x+24.5=34.50\\\\4x=34.50-24.5\\\\4x=10\\\\x = \dfrac{10}{4}\\\\x=2.5[/tex]
Hence, the cost of the hamburgers is $2.5 and chicken burgers are $3.5.
To know more about the System of equations click the link given below.
https://brainly.com/question/24778473
