In one day, a toy store sold 15 toy cars and 20 yo-yos for a total of $190. The next day, the toy store sold 3 toy cars and 12 yo-yos for a total of $102. What is the cost of one toy car?

Answers

Answer 1

Explanation:

Let the price of a toy car be a.

Let the price of a yo-yo be b.

You can solve this problem using simultaneous linear equation.

From the question above, you can form 2 separate equations.

For the first equation,

3 toy cars sold next day = 3a

12 yo-yos sold next day = 12b

Total price = $102

The second equation would be

[tex]3a + 12b = 102[/tex]

Now, we are not finished yet. Make sure that for the first equation, only one of the unknown (a or b) stays on the left-hand side of the equation. Let's try a.

[tex]3a + 12b = 102 \\ 3a = 102 - 12b \\ a = \frac{102 - 12b}{3} \\ a = 34 - 4b[/tex]

Lets move on with finding the second equation.

15 toy cars sold = 15a

20 yo-yos sold = 20b

Total price = $190

So, the second equation would be:

[tex]15a + 20b = 190[/tex]

You don't have to move any unknowns to the other side for the second equation.

Now, take equation 1 and substitute into equation 2. This can be done by replacing the value of a in the second equation with the value of a on the right hand-side of the first equation. For example:

[tex]15a + 20b = 190 \\ 15(34 - 4b) + 20b = 190 \\ 510 - 60b + 20b = 190 \\ 510 - 190 = 60b - 20b \\ 320 = 40b \\ b = \frac{320}{40} \\ = 8[/tex]

Hence, the price of a yo-yo, b, is $8. The price of a toy car is :

[tex]a = 34 - 4b \\ = 34 - 4(8) \\ = 2[/tex]

$2.

Answer 2

The cost of one toy car is $2.

What is a simultaneous linear equation?

Two or more linear equations that all contain the same unknown variables are called a system of simultaneous linear equations. Solving such a system means finding values for the unknown variables which satisfy all the equations at the same time.

Let the price of a toy car be [tex]a[/tex].

Let the price of a Yo-Yo be [tex]b[/tex].

For the first equation,

3 toy cars sold the next day = 3[tex]a[/tex]

12 yo-yos sold the next day = 12[tex]b[/tex]

Total price = $102

The first equation would be

3[tex]a[/tex]+12[tex]b[/tex]=102

Finding the second equation.

15 toy cars sold = 15[tex]a[/tex]

20 yo-yos sold = 20[tex]b[/tex]

Total price = $190

So, the second equation would be:

15[tex]a[/tex]+20[tex]b[/tex]=$190

With the help of these equations, we can find the price of a toy car.

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Answers

Answer:

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Answers

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