Question

1. Form equations for each of the following statement:
a. The length of the rectangle is 7m more than its breadth and its perimeter is 68m.
b. A number divided by 5 gives 7 less than twice the number.
c. A number p multiplied by itself is 7 more than 19.
d. Five eight of a number when added to 3 gives 12.

Answer 1

(a);
Let the breadth of the rectangle be x m.
Its length as in the question = (x+7) m.
Now the perimeter of the rectangle = 2 (length + breadth)
= 2 (x + x +7) = 2 (2x + 14).
it is given that its perimeter is 68 m.
Therefore,$$\begin{gathered} 2\left(2\mathrm{x}+7\right)=68 \\ \Rightarrow 2\mathrm{x}+7=34 \\ \mathrm{It}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{which}\mathrm{represents}\mathrm{the}\mathrm{given}\mathrm{situation}\mathrm{and}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{breadth} \\ \mathrm{and}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{can}\mathrm{be}\mathrm{calculated}\mathrm{using}\mathrm{it}. \end{gathered}$$

(b)
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{y}. \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}\mathrm{when}\mathrm{y}\mathrm{is}\mathrm{divided}\mathrm{by}5\mathrm{it}\mathrm{gives}7\mathrm{less}\mathrm{than}\mathrm{the} \\ \mathrm{twice}\mathrm{of}\mathrm{y}.\mathrm{so}\mathrm{we}\mathrm{can}\mathrm{write} \\ \frac{\mathrm{y}}{5}=2\mathrm{y}-7 \\ \Rightarrow \mathrm{y}=10\mathrm{y}-35 \\ \Rightarrow 9\mathrm{y}-35=0 \end{gathered}$$

(c)
$$\begin{gathered} \mathrm{when}\mathrm{p}\mathrm{is}\mathrm{multiplied}\mathrm{by}\mathrm{itself}\mathrm{it}\mathrm{gives}7\mathrm{more}\mathrm{than}19.\mathrm{So}\mathrm{we}\mathrm{can}\mathrm{write} \\ \mathrm{p}\times \mathrm{p}=19+7 \\ \Rightarrow {\mathrm{p}}^2=26 \end{gathered}$$

(d)
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{z},\mathrm{then}\mathrm{five}\mathrm{eight}\mathrm{of}\mathrm{z}\mathrm{when}\mathrm{added}\mathrm{to}3\mathrm{gives}12 \\ \mathrm{so}\mathrm{we}\mathrm{can}\mathrm{write} \\ \frac{5}{8}\mathrm{z}+3=12 \end{gathered}$$