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On Monday Godswill ate some grapes. On Tuesday he
was hungrier, so he ate 6 more grapes than he had on
Monday. Each day that week, he ate 6 more grapes than the day before. On Friday AFTER he ate his grapes, he realized he had eaten a TOTAL of 100 grapes this week. How many grapes did he eat on Monday? Show all your work and explain how you arrived at your answer.

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luisejr77

Answer: He ate 8 grapes on Monday.

Step-by-step explanation:

Let be "x" the number of grapes Godswill ate on Monday.

You know that he ate 6 more grapes than he had on Monday. This can be expressed with:

[tex]x+6[/tex]

Since each day that week, he ate 6 more grapes than the day before and he realized on Friday he had eaten a total of 100 grapes this week, you can write the following expression and solve for "x":

[tex]x+(x+6)+(x+12)+(x+18)+(x+24)=100\\\\5x+60=100\\\\x=\frac{40}{5}\\\\x=8[/tex]

carlosego

For this case we have to:

Let "x" be the variable that represents the number of grapes Godswill ate on Monday, so we have:

  • Monday:[tex]x[/tex]
  • Tuesday:[tex]x + 6[/tex]
  • Wednesday:[tex](x + 6) + 6 = x + 12[/tex]
  • Thursday[tex]: [(x + 6) +6] + 6 = x + 18[/tex]
  • Friday:[tex]{[(x + 6) +6] +6} + 6 = x + 24[/tex]

Finally we have the following expression:

[tex]x + x + 6 + x + 12 + x + 18 + x + 24 = 100[/tex]

We add similar terms:

[tex]5x + (6 + 12 + 18 + 24) = 100\\5x + 60 = 100\\5x = 100-60\\5x = 40\\x = \frac {40} {5}\\x = 8[/tex]

So, on Monday he ate 8 grapes

Answer:

On Monday he ate 8 grapes.

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