Answer:
7 months
Step-by-step explanation:
Given: Veronica is saving money to buy a saddle for her horse that cost \(\$175\). She plans to save \(\$10\) the first month and then increase the amount she saved by \(\$5\) each month after the first month.
To Find: How many month will it take her to save \(\$175\).
Solution:
Amount veronica has to save for buying saddle \(=\$175\)
Amount increased every month \(\$5\)
Amount saved by veronica in first month \(=\$10\)
Amount saved by veronica in first month \(=\$15\)
Amount saved by veronica in first month \(=\$20\)
Therefore this forms as Arithmetic progression,
Let month it take to save by \(\$175\) veronica is \(=\text{n}\)
Sum of \(\text{n}\) terms in AP is \(\frac{\text{n}}{2}(2\text{a}+(\text{n}-1)\text{d})\)
Putting vales in equation
\(175=\frac{\text{n}}{2}(2\times10+(\text{n}-1)5)\)
\(350=5\text{n}^{2}+15\text{n}\)
\(5\text{n}^{2}+15\text{n}-350=0\)
\(\text{n}^{2}+3\text{n}-70=0\)
\(\text{n}=-10,7\)
As number of months can not be negative,
Hence the it will take \(7\) month for veronica to save \(\$175\) for saddle.
