Doron has a box of red and black toy cars. The ratio of red to black cars is 3:5. He has 15 red cars in the box. how many toy cars are there all together

Ratios is the proportion of two values or two amounts relative to each other. In this case, its between red and black cars where there are 5 black cars for every 3 red cars or conversely, 3 red cars for every 5 black ones.

Ratios can be written with a colon like this x : y or as a fraction [tex]\dfrac{x}{y}[/tex].

They can also be scaled up by any integer value or have both parts of the ratio be multiplied by the same integer to find what bigger x and y values maintains the initial proportion.

Applying Ratios

The problem asks for total number of cars Doron has in this scenario, we know he has 15 red cars but, we must find the number of blacks cars Doron has.

Solution 1: Scale Factors

Here, we're given the initial ratio and a bigger value for the amount of red cars. So, we know that in this scenario, the ratio is scaled up by some factor.

Since 15 is 5 times more than the initial 3, the scenario's ratio must be scaled up by a factor of 5. This means that the number of black cars Doron has must be 5 times the initial value of black cars or 5 x 5 = 25.

We now know the number of black and red cars Doron has, so the total number of cars he has is 15 + 25 or 40.

Solution 2: Algebraic Method

An equation between the initial ratio and the scenario's scaled up ratio can be used to find the number of black cars Doron must have.

[tex]\dfrac{3}{5}=\dfrac{15}{y}[/tex]

[tex]3y=75\\y=25[/tex].

So, Doron has 15 red and 25 black cars, making the total number of cars he owns to be 15 + 25 or 40.