The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5
fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission.
What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)
What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)
2 answers:
Answer:
The solution is (2,6)
Step-by-step explanation:
Let
x-----> the number of hours to change a fuel injection unit
y-----> the number of hours to change a transmission
we know that
5x+10y=70 -----> equation A
8x+8y=64 -----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (2,6)
see the attached figure
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Given:
The graph of a proportional relationship.
To find:
The constant of proportionality, the value of y when x is 24 and the value of x when y is 108.
Solution:
If y is directly proportional to x, then
...(i)
Where, k is the constant of proportionality.
The graph of proportional relationship passes through the point (5,15).
Substituting x=5 and y=15 in (i), we get
Therefore, the constant of proportionality is 3.
Substituting k=3 in (i) to get the equation of the proportional relationship.
...(ii)
Substituting x=24 in (ii), we get
Therefore, the value of y is 72 when x is 24.
Substituting y=108 in (ii), we get
Therefore, the value of x is 36 when y is 108.