Question

Dr. Hoover, a pediatrician, has 3 annual checkups and 2 sick visits scheduled next Tuesday,

Answer 1

Dr. Hoover allot his time on Tuesday for an annual checkup is 147 minutes and for a sick  visit is 42 minutes ​(Total 189 minutes)

On Wednesday appointment,  he allot his time for an annual checkup is 147 minutes and for a sick  visit is 21  minutes ​ (Total 168 minutes)

solution

Let us assume, minutes for annual checkup denoted as x and

minutes for sick visit denoted as y

The equation of Tuesday visit is       $3x + 2y = 189 minutes ------ 1$

The equation of Wednesday visit is    $3x + 1y = 168 minutes ------ 2$

by changing the signs of the equation 2  and  subtract it from the equation 1 we will get   1y = 21 minutes

to substitute y =1 in the equation 2 we get

$3x + 2(21) = 189$

$3x + 42 = 189$

$3x = 189 - 42$

$3x = 147$

$x = 147 ÷ 3 = 49 minutes$

then now we have substitute both x = 49 and y= 21 in equation ----- 2

we will prove that $3x + 2y = 189 = 3 (49) + 2(21) = 189$ $147+ 42 = 189 minutes$

so the Tuesday appointment , the time allotted for an annual checkup is 147 minutes and for a sick  visit is 42 minutes ​(Total 189 minutes)

On Wednesday appointment,  the time allotted for an annual checkup is 147 minutes and for a sick  visit is 21  minutes ​ (Total 168 minutes)