Answer :
To solve the problem of finding [tex]\( q \)[/tex] when [tex]\( p \)[/tex] is equal to 72 given that [tex]\( p \)[/tex] and [tex]\( q \)[/tex] vary inversely, you need to understand the relationship between two quantities that vary inversely.
For quantities that vary inversely, the product of the two quantities is a constant. Mathematically, if [tex]\( p \)[/tex] and [tex]\( q \)[/tex] vary inversely, then:
[tex]\[ p_1 \times q_1 = p_2 \times q_2 \][/tex]
We are given:
[tex]\[ p_1 = 18 \][/tex]
[tex]\[ q_1 = 28 \][/tex]
[tex]\[ p_2 = 72 \][/tex]
We need to determine [tex]\( q_2 \)[/tex].
Let's denote the constant product of [tex]\( p \)[/tex] and [tex]\( q \)[/tex] as [tex]\( k \)[/tex]. According to the inverse variation relationship, the product [tex]\( p_1 \times q_1 \)[/tex] should equal the product [tex]\( p_2 \times q_2 \)[/tex]:
[tex]\[ k = p_1 \times q_1 \][/tex]
First, we find [tex]\( k \)[/tex]:
[tex]\[ k = 18 \times 28 \][/tex]
Calculate the product:
[tex]\[ 18 \times 28 = 504 \][/tex]
Since this is an inverse variation, the constant [tex]\( k \)[/tex] remains the same. Now we need to use this constant to find [tex]\( q_2 \)[/tex] when [tex]\( p_2 \)[/tex] is 72:
[tex]\[ p_2 \times q_2 = k \][/tex]
[tex]\[ 72 \times q_2 = 504 \][/tex]
Now, solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{504}{72} \][/tex]
Perform the division:
[tex]\[ q_2 = 7 \][/tex]
Thus, when [tex]\( p \)[/tex] is 72, [tex]\( q \)[/tex] is 7.
For quantities that vary inversely, the product of the two quantities is a constant. Mathematically, if [tex]\( p \)[/tex] and [tex]\( q \)[/tex] vary inversely, then:
[tex]\[ p_1 \times q_1 = p_2 \times q_2 \][/tex]
We are given:
[tex]\[ p_1 = 18 \][/tex]
[tex]\[ q_1 = 28 \][/tex]
[tex]\[ p_2 = 72 \][/tex]
We need to determine [tex]\( q_2 \)[/tex].
Let's denote the constant product of [tex]\( p \)[/tex] and [tex]\( q \)[/tex] as [tex]\( k \)[/tex]. According to the inverse variation relationship, the product [tex]\( p_1 \times q_1 \)[/tex] should equal the product [tex]\( p_2 \times q_2 \)[/tex]:
[tex]\[ k = p_1 \times q_1 \][/tex]
First, we find [tex]\( k \)[/tex]:
[tex]\[ k = 18 \times 28 \][/tex]
Calculate the product:
[tex]\[ 18 \times 28 = 504 \][/tex]
Since this is an inverse variation, the constant [tex]\( k \)[/tex] remains the same. Now we need to use this constant to find [tex]\( q_2 \)[/tex] when [tex]\( p_2 \)[/tex] is 72:
[tex]\[ p_2 \times q_2 = k \][/tex]
[tex]\[ 72 \times q_2 = 504 \][/tex]
Now, solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{504}{72} \][/tex]
Perform the division:
[tex]\[ q_2 = 7 \][/tex]
Thus, when [tex]\( p \)[/tex] is 72, [tex]\( q \)[/tex] is 7.
