Respuesta :
Step 1. As a reference to solve this problem, we will call the original quantity ''x''
[tex]x\longrightarrow\text{original quantity}[/tex]Step 2. The first discount applied is 70% --> to calculate this discount we multiply our original quantity by 0.7:
[tex]70\text{ percent discount }\longrightarrow0.7x[/tex]Step 3. Now we apply the second discount in the series of discounts which is a 10% discount. We need to multiply the previous result by 0.1:
[tex]10\text{ percent discount}\longrightarrow0.1\times0.7x\longrightarrow0.07x[/tex]Step 4. The last of the discounts is a 20% discount over the already discounted amount, so again we multiply the previous result but this time for 0.2 to find the 20% discount:
[tex]20\text{percent discount}\longrightarrow0.2\times0.07x\longrightarrow0.014x[/tex]Step 5. Add all of the discounts:
[tex]0.7x+0.07x+0.014x[/tex]The result is:
[tex]0.784x[/tex]The equivalent discount is 0.784 of the original amount ''x''.
We can multiply this decimal number by 100 to find the equivalent percent discount:
[tex]0.784\times100=78.4[/tex]The equivalent discount is 78.4%
Answer: 78.4%
