Babysitting Pay

Algebra Level 1

Joanna was paid $100 for babysitting five days after school for the Zorn family. Each day Mrs. Zorn paid her $5 more than the day before. How much money did she earn on the first day?

$20 $30 $15 $10

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Chung Kevin by Chung Kevin , 45, Australia

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3 solutions

It is arithmetic series with increment of $5 with 5 terms. If first day he was paid $x, 2nd day he was paid $5 more the fifth day he was paid $(5-1) * 5=20 more. So he was paid ( 5 + 20 ) ∗ 4 2 = $ 50 \dfrac { (5+20) * 4}2=\$50 extra.... So 100=$50+5x. .... So x=10.
O R ~~~OR~~

Using the formula, where S is the sum, x the first term, d the increment, and n the number of terms, S = n ∗ { 2 x + ( n − 1 ) ∗ d } 2 S=\dfrac{n*\{2x+(n-1)*d\}}{ 2} . In our case S=100, n=5, d=5. ∴ 100 = 5 ∗ { 2 x + 4 ∗ 5 } 2 . S o l v i n g , x = 10. \therefore~100=\dfrac{5*\{2x+4*5\}} 2.~~ Solving,~~ x=10.

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Uahbid Dey
Aug 20, 2015

f + ( f + 5 ) + ( f + 10 ) + ( f + 15 ) + ( f + 20 ) = 100 f + (f+5) + (f+10) + (f+15) + (f+20) = 100 = > 5 f + 50 = 100 => 5f + 50 = 100 = > 5 f = 50 => 5f = 50 = > f = 10 => f = 10

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Or you can use the terms: a − 10 , a − 5 , a , a + 5 , a + 10 a - 10, a- 5, a , a + 5 , a + 10 such that their sum is is 100.

Chung Kevin - 5 years, 9 months ago
Ds Faisal
Aug 20, 2015

5*X+5+10+15+20=100; X=payment on first day

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