Question

I need help on question 27

Answer 1

Question:

A =
`(1)/(2)h(b_(1) +b_(2) )`

If A = 136 when
`b_(1)` = 7 and h = 16, find
`b_(2)`

Givens:

We are given the equation that we are working with:

A =
`(1)/(2)h(b_(1) +b_(2) )`

We are given certain values that the variables, in this case, are equal to:

A = 136

`b_(1)` = 7

h = 16

Steps:

Substitute the given variables in the given equation for the corresponding numbers:

A =
`(1)/(2)h(b_(1) +b_(2) )`

136 =
`(1)/(2)` * 16 (7 +
`b_(2)`)

We know all the values in the equation except
`b_(2)`. In order to find
`b_(2)` we must isolate it on one side of the equation

136 = 8 (7 +
`b_(2)`)

`(136)/(8)` =
`(8 (7 + b_(2)) )/(8)`

17 = 7 +
`b_(2)`

17 - 7 = 7 - 7 +
`b_(2)`

10 =
`b_(2)`

Check:

If
`b_(2)` is equal to 10 then if we plug it back into the given equation both sides of the equation should equal each other. Remember to use PEMDAS

136 =
`(1)/(2)` * 16 (7 +
`b_(2)`)

136 =
`(1)/(2)` * 16 (7 + 10)

136 =
`(1)/(2)` * 16 (17)

136 = 8 (17)

136 = 136

`b_(2)` = 10