Luna and ginny each cast magic spells. the ratio of
spells luna casts to spells ginny casts is represented in
the tape diagram
luna-4
ginny-5
based on the ratio, what is the number of spells
ginny casts when luna casts 20 spells?
spells

The number of spells  Ginny casts when Luna casts 20 spells is 25

Step-by-step explanation:

Luna and Ginny each cast magic spells.

The ratio of  spells Luna casts to spells Ginny casts = 4:5

Let the ratio be x

So, Luna casts = 4x

Ginny casts = 5x

We are supposed to find what is the number of spells  Ginny casts when Luna casts 20 spells

So, 4x=20

Ginny casts =

Hence The number of spells  Ginny casts when Luna casts 20 spells is 25

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.