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Trina is saving to buy a new phone. She has two options. The first option is to put $400 away initially and save $20 every month. The second option is to put $100 away initially and save $40 every month. After how many months, m, would Trina save the same amount using either option? How much would she save with either option? Write and solve an equation to show your work.

Answer :

Total amount saved in 1st case :

[tex]S_1=400+20t_1[/tex]

Total amount saved in 2nd case :

[tex]S_2=100+40t_2[/tex]

( Here [tex]t_1 \ and\ t_2[/tex] are number of months )

Let, after x months the amount saved in both cases is same.

So,

[tex]S_2=S_1\\\\100+40x=400+20x\\\\20x = 300\\\\x = 15\ months[/tex]

Amount saved :

[tex]S_1=400+20(15) =\$ 700[/tex]

[tex]S_2=100+40( 15)= \$700[/tex]

Hence, this is the required solution.

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