Question

bananas cost $1.50 per pound, and guavas cost $3.00 per pound. kiran spends $12 on fruit to for a breakfast his family is hosting. let b be the number of pounds of bananas kiran buys and g be the number of pounds of guavas he buys. a. write an equation relating the two variables. b. rearrange the equation so b is the independent variable. c. rearrange the equation so g is the independent variable.

Answer 1

let
b -------> the number of pounds of bananas
g -------> the number of pounds of guavas

we know that
$1.5b+$3g=$12

Part a) write an equation relating the two variables

the answer Part a) is
1.5b+3g=12

Part b) rearrange the equation so b is the independent variable
1.5b+3g=12---------> clear variable g
3g=12-1.5b
g=(12/3)-(1.5/3)b------> g=4-0.5b

the answer Part b) is
g=4-0.5b   ( b is the independent variable)

Part c) rearrange the equation so g is the independent variable
1.5b+3g=12---------> clear variable b
1.5b=12-3g
b=(12/1.5)-(3/1.5)g--------> b=8-2g

the answer Part c) is 
b=8-2g    ( g is the independent variable)

Answer 2

Here we will find and rewrite a linear equation, the answers are:

• a) b*$1.50 + g*$3.00 = $12
• b) g =  4 - b*0.5
• c) b = 8 - g*2

How to work with linear equations?

The variables that we will use are:

• b = pounds of bananas bought.
• g = pounds of guavas bought.

a)

We know that Kiran spends $12, then we have the equation:

b*$1.50 + g*$3.00 = $12

b) If b must be the independent variable, then we need to isolate g:

g*$3.00 = $12 - b*$1.50

g = ($12 - b*$1.50)/$3.00 = 4 - b*0.5

c) Now we want g to be the independent variable, so this time we need to isolate b.

b*$1.50 = $12 - g*$3.00

b = ($12 - g*$3.00)/$1.50

b = 8 - g*2

If you want to learn more about linear equations, you can read:

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