Question

Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?
The equation_____models the scenario.
Hans will plant______snapdragons.

Answer 1

The equation is $x+y=45$

For 29 daisies, we have $y=29$
$\rightarrow x+29=45$
$\rightarrow x=16$ snapdragons

Answer 2

Answer: The equation $x+y=45$ models the scenario.

Hans will plant 16 snapdragons.

Step-by-step explanation:

From the given table, it can be seen that there is constant change in y with respect to x.

i.e. for every one increment of x, there is decrease in y by one quantity.

Thus, the given equation must be linear.

The linear equation is given by :-

$y=mx+c$, where m, is the rate of change of y w.r.t. x.

Now, the rate of change of function will be :-

$m=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{33-34}{12-1}=-1$

Put m=-1, x=11 and y = 34, we get

$34=-11+c\\\\\Rightarrow\ c=34+11=45$

Thus the equation models the scenario:

$y=-x+45\\\\\Rightarrow\ x+y=45$

Now, to find the number of snapdragons by planting 29 daisies, put y=29 in the above equation,

$29=-x+45\\\\\Rightarrow\ x=45-29=16$