Hailey bought a 9 ft piece of ribbon that she will cut into 2/3 ft long pieces. How many 2/3 ft pieces can Hailey cut?
1 answer:
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we have
Let's Isolate the variable y in each of the cases and then compare with Fiona's equation to determine the solution of the problem
case A)
Multiply by both sides
Divide by both sides
therefore
the case A) is not equal to Fiona's equation
case B)
Multiply by both sides
Divide by both sides
therefore
the case B) is not equal to Fiona's equation
case C)
Multiply by both sides
Divide by both sides
therefore
the case C) is not equal to Fiona's equation
case D)
Multiply by both sides
Divide by both sides
therefore
the case D) is equal to Fiona's equation
<u>the answer is</u>
Answer:
2/3
Step-by-step explanation:
Let's define z = x-y, so solving for z will tell us exactly what we want to know. Then we can substitute for x: x = z+y, and our equations become ...
7(z+y)+3y = 8 ⇒ 7z +10y = 8
6(z+y)-3y = 5 ⇒ 6z +3y = 5
We can eliminate the y-variable by subtracting 3 times the first equation from 10 times the second:
10(6z +3y) -3(7z +10y) = 10(5) -3(8)
60z +30y -21z -30y = 50 -24 . . . . eliminate parentheses
39z = 26 . . . . collect terms
z = 26/39 = 2/3 . . . . . divide by the coefficient of z and reduce
The value of x - y is 2/3.
_____
The attached graph shows (x, y) = (1, 1/3), so x - y = 1 - 1/3 = 2/3.
