The table below shows the amount of money earned by two different workers over 5 consecutive days.
Donald's Earnings, x
(dollars) Fallon's Earnings, y
(dollars)
38 45
43 50
48 55
53 60
58 65
Which equation best represents Fallon's earnings in terms of Donald's earnings?
A.
x = 7y
B.
y = 7x
C.
y = x + 7
D.
x = y + 7
B. y = 7x
The graph below shows raffle ticket sales and the money earned from the sales.
Which of the following is the independent variable?
A.
both tickets sold and money earned
B.
tickets sold
C.
money earned
D.
neither tickets sold nor money earned
B. tickets sold
Look at the relationship between a and b.
a 6 7 8 9
b 48 47 46 45
Which equation below describes the relationship between a and b?
A.
b = 54 - a
B.
b = 42 + a
C.
b = 288 ÷ a
D.
b = 8 × a
A. b = 54 - a
explain
In the given data, the values of b decrease by 1 for every unit increase in a. So, we can say that b is inversely proportional to a.
To find out the equation that describes the relationship between a and b, we can use the formula for inverse proportionality which is given as:
a x b = k
where k is a constant.
Plugging in the given values of a and b, we get:
6 x 48 = k
7 x 47 = k
8 x 46 = k
9 x 45 = k
Solving each equation for k, we get:
k = 288
k = 329
k = 368
k = 405
Now, we can use any of these values of k to write the final equation. Let's use the first value of k which is 288.
a x b = 288
b = 288 ÷ a
Multiplying both sides by -1, we get:
-b = -288 ÷ a
Adding 54 to both sides, we get:
54 - b = 54 - 288 ÷ a
54 - b = (54a - 288) ÷ a
54a - a x b = 288
Substituting the given values of a and b, we get:
54a - 288 = 6 x 48
54a - 288 = 7 x 47
54a - 288 = 8 x 46
54a - 288 = 9 x 45
Solving each equation for a, we get:
a = 6
a = 7
a = 8
a = 9
We can see that the value of a is decreasing by 1 for every unit increase in b. So, we can write:
a = 54 - b
Putting this equation in the form y = mx + c, we get:
b = -a + 54
or, rearranging:
b = 54 - a
Hence, the equation that describes the relationship between a and b is b = 54 - a.