Question

Matt wants to buy a television. If he pays cash, he gets a discount of 7%. If he pays with a loan he has to pay an extra 10% in interest. The difference between the two methods is $49.98. Find the cost of the television. PS: the final answer is $294, I just need the steps please!!! ​

Answer 1

`\Large \implies\colorbox{cyan}{\$294}`

Step-by-step explanation :

Step 1) : Based on the given conditions, formulate :

`\bf \longrightarrow{x * (10\% + 7\%) = \$49.98}`

Step 2) : Solve the equation :

`\bf \longrightarrow{x * (10\% + 7\%) = \$49.98 }\\ \\ \bf \longrightarrow{x * 17\% = \$49.98} \\ \\ \bf \longrightarrow{ x * 0.17 = \$49.98} \\ \\ \bf \longrightarrow{ 0.17x = \$49.98} \\ \\ \bf \longrightarrow{ x = (\$49.98)/(0.17) } \\ \\ \bf \longrightarrow{x = (\$49.98 * 100)/(0.17 * 100) } \\ \\ \bf \longrightarrow{x = { \cancel{(\$4998)/(17) }} }\\ \\ \bf \longrightarrow{ x = \boxed{ \bf \pink{\$294} }\: \underline{ \red{ans.}}}`