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During the summer, Jody earns [tex]$10 per hour babysitting and $[/tex]15 per hour doing yardwork. This week she worked 34 hours and earned $410. If [tex]\( x \)[/tex] represents the number of hours she babysat and [tex]\( y \)[/tex] represents the number of hours she did yardwork, which system of equations models this situation?

A.
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 10x + 15y = 410 \][/tex]

B.
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 10x + 15y = 34 \][/tex]

C.
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 15x + 10y = 410 \][/tex]

D.
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 15x + 10y = 34 \][/tex]

Sagot :

GinnyAnswer
Let's break down the problem to identify the correct system of equations that models Jody's work hours and earnings.

First, we define the variables:
- Let [tex]\( x \)[/tex] be the number of hours Jody babysat.
- Let [tex]\( y \)[/tex] be the number of hours she did yardwork.

Given conditions:
1. Jody worked a total of 34 hours combining babysitting and yardwork. This can be written as:
[tex]\[ x + y = 34 \][/tex]

2. Jody earns [tex]\(\$10\)[/tex] per hour for babysitting and [tex]\(\$15\)[/tex] per hour for yardwork. The total earnings for the week were
[tex]\(\$410\)[/tex]. This can be written as:
[tex]\[ 10x + 15y = 410 \][/tex]

Now let's match these equations to the given options:

A.
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 10x + 15y = 410 \][/tex]

B.
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 10x + 15y = 34 \][/tex]

C.
[tex]\[ x + y = 34 \][/tex]
[tex]\[ 15x + 10y = 410 \][/tex]

D.
[tex]\[ x + y = 410 \][/tex]
[tex]\[ 15x + 10y = 34 \][/tex]

Analyzing these options, only option A represents the correct system of equations matching our conditions:

[tex]\[ x + y = 34 \][/tex]
[tex]\[ 10x + 15y = 410 \][/tex]

Therefore, the correct answer is option A.
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