Question

Sean wrote the equation 9.25 = 5m, where m is the cost per pound, to show the relationship between the total cost, $9.25, and the number of pounds of pears, 5, he bought at quick mart

Answer 1

Explanation:

The complete question is in a comment above. The statements says that:

• Sean wrote the equation $9.25=5m$
• $m$ is the cost per pound.
• The equation show the relationships between the total cost, $9.25, and the number of pounds of pears.

So we are asked to write an write an equation to show the cost y of x pounds of pears. In other words, we need to write an equation such that y is given in terms of x, where x is the pounds of pears. So:

$y=f(x)$

From the equation we can determine $m$ as:

$m=\frac{9.25}{5}=1.85$

So each pound costs $1.85. The equation tells us that 5 pounds of pears result costs $9.25. Then, by proportion:

$\frac{y}{x}=\frac{9.25}{5} \\ \\ y=1.85x$

So choosing the number of pounds as 0, 1, 2, 3, 4, 5, the table would be:

$\begin{array}{cc}x(\text{Number of pounds}) & y(\text{Cost in dollars})\\0 & 0\\1 & 1.85\\2 & 3.7\\3 & 5.55\\4 & 7.4\\5 & 9.25\end{array}$

From the table we can know that the graph is a line. that passes through all these points. Since this line passes through the origin, then y varies directly as x (Direct Proportion).