Respuesta :
So here is the answer. Initially, Ed's toy cars compared to Pete's toy cars was 5:2. So for every 5 cars that Ed has, Pete has 2. Now that Ed gave 30 cars to Pete. So here it goes. The total number of ratio units is 5+2=7, so each will have an equal number if they both have 3.5 ratio units. That is, if Ed transfers to Pete 1.5 ratio units, their car counts will be equal. Thus 1.5 ratio units = 30 cars, or 1 ratio unit = 20 cars. Therefore, this makes 7*20 cars = 140 cars.
Hope this helps.
Hope this helps.
A ratio shows us the number of times a number contains another number. The number of total toy cars with Ed and Pete is 140.
What is a Ratio?
A ratio shows us the number of times a number contains another number.
Let the number of toy cars with Ed be represented by x, while the number of toy cars with Pete is represented by y.
As mentioned that the ratio of Ed’s toy cars to Pete’s toy cars was 5:2. Therefore, the ratio can be written as,
[tex]\dfrac xy=\dfrac{5}{2}[/tex]............... Eqn. 1
Now, after Ed gave 30 toy cars to Pete, they each had an equal number of toy cars. Therefore, we can write,
[tex]\dfrac {x-30}{y+30}=1[/tex]............... Eqn. 2
If we solve the equation 1 to get the value of x, we will get,
[tex]\dfrac {x}{y}=\dfrac{5}{2}\\\\x=\dfrac{5y}{2}\\\\ x=2.5y[/tex]
Substitute the value of x in equation 2, we will get,
[tex]\dfrac {x-30}{y+30}=1\\\\\\ \dfrac {2.5y-30}{y+30}=1\\\\\\2.5y-30=y+30\\\\2.5y-y=30+30\\\\1.5y = 60\\\\y=\dfrac{60}{1.5} = 40[/tex]
Now substitute the value of x in equation 1,
[tex]\dfrac xy=\dfrac{5}{2}\\\\\dfrac {x}{40}=\dfrac{5}{2}\\\\x=\dfrac{5 \times 40}{2}\\\\x = 100[/tex]
Further, the number of total toy cars with Ed and Pete can be written as,
[tex]\text{Total number of toys}=x+y\\\\\text{Total number of toys}=100+40 = 140[/tex]
Hence, the number of total toy cars with Ed and Pete is 140.
Learn more about Ratios:
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