John and Kevin each bought apples at the store. John bought three more than twice the number of apples Kevin bought. If they bought 21 apples combined, how many apples did Kevin buy?

Let x be the amount of apples that Kevin bought.

It says that john buys three more than twice the amount of apples that kevin buys, so 3 + 2x apples.

They bought 21 apples total, so x + 3 + 2x=21

Collecting like terms gives 3x+3=21

Subtracting 3 from both sides gives 3x=18 and then dividing both sides by 3 gives x=6

x is the amount of apples kevin bought, so kevin bought 6 apples

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dubeyshailja64 dubeyshailja64 · Answer 2 · 2022-01-13T11:52:08+01:00

A linear equation refers to an equation whose variable has 1 as its highest power. It can be also referred as one-degree equation.

The standard form of a linear equation in one variable is:

[tex]\rm ax + b = 0[/tex]

For the given question, the equation will be:

[tex]\begin{aligned} \rm 3x + 3 &= 21\\\\3x - 18 &= 0\end[/tex]

and the number of apples bought by Kevin and John is 6 and 18 respectively.

To calculate the above, we need following calculations:

Let the number of apples bought by Kevin be x

Therefore, apples bought by John will be [tex]\rm2x + 3[/tex]. ...eq. 1

Since total number of apples bought by Kevin and John is 21.

Equation will be:

[tex]\rm \begin{aligned} x + 2x + 3 &= 21\\3x + 3 &= 21\\3x + 3 - 21 &= 0\\3x - 18 &= 0\end[/tex]

To solve the above equation, we will equate both sides as:

[tex]\rm3x = 18[/tex]

Dividing both sides by 3:

[tex]\begin{aligned} \dfrac{3x}{3} &= \dfrac{18}{3}\\x &= 6\end[/tex]

Therefore,number of apples bought by Kevin is 6

By equation 1, number of apples bought by John will be:

[tex]\begin{aligned} \rm2x + 3 &= 2(6) + 3\\&= 15\end[/tex]

The correct answer is 6 and 15 apples bought by Kevin and John respectively.

Learn more about Linear equations here:

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