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Two girls have 91 pence between them. If the first has six times as much as the other, how much does the second have?

Sagot :

Certainly! Let's determine how much each girl has step-by-step.

1. Define Variables:
- Let the amount of money the second girl has be [tex]\( x \)[/tex].
- Therefore, the first girl has 6 times as much as the second girl, which is [tex]\( 6x \)[/tex].

2. Set Up the Equation:
- Together, they have a total of 91 pence.
- So, we can set up the equation based on their combined money:
[tex]\[ x + 6x = 91 \][/tex]

3. Combine Like Terms:
- Simplify the equation:
[tex]\[ 7x = 91 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], divide both sides of the equation by 7:
[tex]\[ x = \frac{91}{7} \][/tex]
- This gives us:
[tex]\[ x = 13 \][/tex]

Thus, the second girl has 13 pence.

5. Substitute to Find the First Girl's Amount:
- Since the first girl has 6 times as much as the second girl:
[tex]\[ 6x = 6 \times 13 = 78 \][/tex]

So, the first girl has 78 pence.

In conclusion, the second girl has 13 pence.