Question 107·Medium·Linear Equations in One Variable
Laura is saving to buy a bicycle that costs $260. She currently has $85 and plans to save the same amount each week. If she reaches her goal in 7 weeks, how much money, in dollars, will she need to save each week?
(Express the answer as an integer)
For savings or cost-sharing problems like this, first subtract any amount already saved or paid from the total to find how much is left. Then, if the situation says the same amount is added each week (or each month, each person, etc.), divide the remaining amount by the number of equal parts (weeks, months, people). Writing a quick equation, like , helps avoid mistakes and makes the arithmetic straightforward.
Hints
Focus on what is already saved
She does not need to save the full $260. How much more does she need beyond the $85 she already has?
Translate the situation into an equation
If she saves the same amount each week for 7 weeks to reach the remaining needed amount, how can you write that with a variable for the weekly savings?
Isolate the variable
Once you have an equation like , what operation will isolate ?
Desmos Guide
Compute the remaining amount needed
Type 260-85 into Desmos and note the result; this is how much more money Laura must save.
Divide by the number of weeks
Take the result from step 1 and divide by 7 in Desmos by typing (260-85)/7. The output is the amount she needs to save each week.
Step-by-step Explanation
Identify how much more money Laura needs
Laura needs a total of $260 and already has $85.
Compute how much more she still needs to save:
So, she still needs $175 in additional savings.
Relate the remaining amount to the number of weeks
She will save the same amount each week for 7 weeks, and that total must be the remaining $175.
Let be the amount she saves each week. Then the situation can be written as the equation:
This means 7 weeks of saving dollars per week adds up to $175.
Solve for the weekly savings
To find , divide both sides of the equation by 7:
Now compute the division:
So, Laura needs to save 25 dollars per week.