Three girls made necklaces using beads. Jamie used 5 times as many beads as Carmen did. Allison used 8 more than 3 times as many beads as Carmen did. The total number of beads used by the three girls was 143. Which equation can be solved to find the number of beads (n) that Carmen used to make her necklace?

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05-10-2018
Mathematics

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Three girls made necklaces using beads. Jamie used 5 times as many beads as Carmen did. Allison used 8 more than 3 times as many beads as Carmen did. The total number of beads used by the three girls was 143. Which equation can be solved to find the number of beads (n) that Carmen used to make her necklace?

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valman67 valman67 · Answer 1 · 2018-10-06T00:37:47+02:00

Carmen is X
Jamie will be X(Carmen) times 5
Allison will be X(Carmen) times 3 plus 8.

So the equation will be
[tex]x + 5x + 3x + 8 = 143[/tex]

To solve, we will need to combine the I'd
[tex]x + 5x + 3x = 9x[/tex]
[tex]9x + 8 = 143[/tex]
Then we subtract 8 from both sides

[tex]9x = 135[/tex]
divide both sites by 9
[tex]9x \div 9x = x \\ 135 \div 9 = 15[/tex]
Carmen has 15. Now we just need to plug in the information we had from earlier.

[tex]15 \times 5 = 75[/tex]
Jamie used 75

[tex]15 \times 3 + 8 \\ 45 + 8 \\ 53[/tex]
Allison used 53