Lea buys 20 picture frames. Some are 4 in. by 6 in. frames which cost $5.80 each, and the rest are 5 in. by 7 in. frames that cost $9.60 each. She spends a total of $80.80.

Which equation models this situation?

Let \( f \) represent the number of 4 in. by 6 in. frames she buys.

A. \( 9.6f + 5.8(20) = 80.8 \)

B. \( 5.8f + 9.6(20 - f) = 80.8 \)

C. \( (5.8 + 9.6)(20 - f) = 80.8 \)

D. \( 9.6f + 5.8(f + 20) = 80.8 \)

To find the answer we have to slowly analyze the command. For surely on the one side we want to have total cash spent, so 80.8 W e kn o wt ha tt h ere a re 2 t y p eso ff r am es 5 , 80 and 9.60 . W e kn o wt oo , t ha t f i s t h e n u mb ero ff r am es 5.80 bought. Simply, to find the cash spent on those frames we have to just mulitply 5.80 t im es f , so w eo b t ain [ t e x ] f ∗ 5.8 [ / t e x ] . W ec an s a y t ha t n u mb ero f bi gg er f r am es i s 20 − f . S o t o f in d c a s h s p e n t o nbi gg er f r am es w e ha v e t o m u lt i pl y 9.60 times (20-f), so 9.60 ∗ ( 20 − f ) Now we can just add cost of all frames together f ∗ 5.80 + 9.60 ( 20 − f ) And we know that is equal to 80.8, so f ∗ 5.80 + 9.60 ( 20 − f ) =80.8
As we can see, the answer is b.

Answered by macio06 | 2024-06-10

The equation that models Lea's frame purchases is 5.8 f + 9.6 ( 20 − f ) = 80.8 from option B. This represents the total cost based on the number of each type of frame. Thus, option B is the correct choice.
;

Answered by macio06 | 2024-12-26