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APPL ICATION: Business Decisions and Solving by Elimination Sibling Savings and her sister Maryam are excited to begin saving for a new bike they can share. Their aunt said that if 710 total. they saved up enough money, she would split the cost with them and pay for half.The new bike will cost The girls concluded that they would have just enough if they saved the money from 2 days' worth of Leyla's paper route and 3 days' worth of Maryam's dog walking job. Maryam has to work a little more because her each earning/obpays 5 less than Leyla's paper route. How much do the paper route and dog walking jobs each earn per day? 1. Write a system of equations to model this problem. 2. Solve this system of equations using whichever method you choose. Show your work. 3.How much do the paper route and dog walking earn the girls? 4.Would their wages be higher or lower if it actually took them 3 days of Leyla's paper route and days of Maryam's dog walking job?

Question

APPL ICATION: Business Decisions and Solving by Elimination Sibling Savings and her sister Maryam are excited to begin saving for a new bike they can share. Their aunt said that if 710 total. they saved up enough money, she would split the cost with them and pay for half.The new bike will cost The girls concluded that they would have just enough if they saved the money from 2 days' worth of Leyla's paper route and 3 days' worth of Maryam's dog walking job. Maryam has to work a little more because her each earning/obpays 5 less than Leyla's paper route. How much do the paper route and dog walking jobs each earn per day? 1. Write a system of equations to model this problem. 2. Solve this system of equations using whichever method you choose. Show your work. 3.How much do the paper route and dog walking earn the girls? 4.Would their wages be higher or lower if it actually took them 3 days of Leyla's paper route and days of Maryam's dog walking job?

APPL ICATION: Business Decisions and Solving by Elimination Sibling Savings and her sister Maryam are excited to begin saving for a new bike they can share. Their aunt said that if 710 total. they saved up enough money, she would split the cost with them and pay for half.The new bike will cost The girls concluded that they would have just enough if they saved the money from 2 days' worth of Leyla's paper route and 3 days' worth of Maryam's dog walking job. Maryam has to work a little more because her each earning/obpays 5 less than Leyla's paper route. How much do the paper route and dog walking jobs each earn per day? 1. Write a system of equations to model this problem. 2. Solve this system of equations using whichever method you choose. Show your work. 3.How much do the paper route and dog walking earn the girls? 4.Would their wages be higher or lower if it actually took them 3 days of Leyla's paper route and days of Maryam's dog walking job?

Solution

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Answer

### The paper route earns \$14 per day, and the dog walking job earns \$9 per day. Their wages would be higher if it took 3 days of Leyla's paper route and 2 days of Maryam's dog walking job.

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## Step 1: Define Variables and Set Up Equations<br />### Let $x$ be the daily earnings from Leyla's paper route, and $y$ be the daily earnings from Maryam's dog walking job. The total cost of the bike is $\$110$, and their aunt will pay half, so they need to save $\frac{110}{2} = \$55$. We know that 2 days of Leyla's work plus 3 days of Maryam's work equals this amount, and Maryam earns $\$5$ less than Leyla per day. Thus, we have the system:<br />\[<br />\begin{align*}<br />2x + 3y &= 55 \\<br />y &= x - 5<br />\end{align*}<br />\]<br /><br />## Step 2: Substitute and Solve for One Variable<br />### Substitute $y = x - 5$ into the first equation:<br />\[<br />2x + 3(x - 5) = 55<br />\]<br />Simplify and solve for $x$:<br />\[<br />2x + 3x - 15 = 55 \\<br />5x - 15 = 55 \\<br />5x = 70 \\<br />x = 14<br />\]<br /><br />## Step 3: Solve for the Second Variable<br />### Use the value of $x$ to find $y$:<br />\[<br />y = x - 5 = 14 - 5 = 9<br />\]<br /><br />## Step 4: Analyze Alternative Scenario<br />### If it took 3 days of Leyla's paper route and 2 days of Maryam's dog walking job, the equation would be:<br />\[<br />3x + 2y = 55<br />\]<br />Substitute $x = 14$ and $y = 9$:<br />\[<br />3(14) + 2(9) = 42 + 18 = 60<br />\]<br />This exceeds the required $\$55$, indicating higher wages.
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