SOLUTION: Anna's farm picked a total of 310 pumpkins. Anna separated the pumpkins into small and large. She sold the small pumpkins for $3 each and the large ones for $9 each. She sold all o

Algebra ->  Human-and-algebraic-language -> SOLUTION: Anna's farm picked a total of 310 pumpkins. Anna separated the pumpkins into small and large. She sold the small pumpkins for $3 each and the large ones for $9 each. She sold all o      Log On


   

Question 107336: Anna's farm picked a total of 310 pumpkins. Anna separated the pumpkins into small and large. She sold the small pumpkins for $3 each and the large ones for $9 each. She sold all of the pumpkins for total sales of $1,950. How many small and large pumpkins did Anna originally pick?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L: number of large pumpkins
S: number of small pumpkins
Total of 310 pumpkins.
1.L%2BS=310
She sold the small pumpkins for $3 each and the large ones for $9 each. She sold all of the pumpkins for total sales of $1,950.
2.9L%2B3S=1950
Use equation 1 and solve for L.
1.L%2BS=310
L=310-S
Substitute that value in equation 2 and solve for S.
2.9L%2B3S=1950
9%28310-S%29%2B3S=1950
9%28310%29-9S%2B3S=1950
2790-6S=1950
2790-6S%2B6S=1950%2B6S
2790=1950%2B6S
2790-1950=1950-1950%2B6S
840=6S
840%2F6=S
S=140
From above
L=310-S
L=310-140
L=170
Check your answers with your original equations.
1.L%2BS=310
170%2B140=310
310=310
Your answer leads to a true statement.
Good answer.
2.9L%2B3S=1950
9%28170%29%2B3%28140%29=1950
1530%2B420=1950
1950=1950
Your answer leads to a true statement.
Good answer.
Anna picked 170 large pumpkins and 140 small pumkins.