Math
posted by Tam
Sophia buys an eqaul number of oranges and pears for a party. The oranges are bought at a price of 7 for $2 and the pears are bought at a price of 5 for $3. She pays $33 more for the pears than the oranges. How much does Sophia pay in all? How many oranges and pears does she buy altogether?

Henry
X = # of oranges.
X = # of pears.
($2/7) * X = $Y
Multiply both sides by 7:
2x = 7y
Eq1: 2x  7y = 0
($3/5) * X = y + 33
Multiply both sides by 5:
3x = 5y + 165
Eq2: 3x  5y = 165
Multiply Eq1 by 3 and Eq2 by 2 and add:
+6x  21y = 0
6x + 10y = 330
Sum: 11y = 330
Y = $30 = Cost of oranges
Y+33 = 30 + 33 = $63 = Cost of pears
Total cost = 30+63 = $93.
In Eq1, replace y with 30:
2x  7*30 = 0
2x = 210
X = 105 of each fruit.
Tot. fruit = 2*105 = 210.
Respond to this Question
Similar Questions

Math Mania
A fruit stand carries apples, oranges, lemons, and pears. There are twice as many apples as oranges and 3 times as many lemons as pears. If there are 3 more oranges than pears, and p represents the number of pears, which of the following … 
math
jasmine bought 26 pieces of fruit.she bought 6 oranges.she bought twice as many apples as oranges,and twice as many oranges as bananas.she also bought some pears. 
math
a crate contains apples, pears, and oranges.There are 184 apples and pears and 248 apples and oranges. there are 3 times as many oranges as pears. how many apples are in the crate? 
Algebra
If you bought 6 pears and 20 oranges and then bought 11 pears and 12 oranges and spent the same each time, how much do oranges cost if the pears are 80 cents each? 
Maths algebra
Wilma went to the local market and bought 3 lemons and 5 oranges for $2.40.The same day and for the same price ,Fran bought 4 lemons and 7 oranges for $3.31.What was the prices per lemon and the price per orange? 
math
Alex bought twice as many pears as apples. He bought 4 more pears than oranges. He bought 6 apples. How many oranges did Alex buy? 
math/ratio
apples,oranges and pears are packed into a basket in the ratio 3:5:1. there are 12 more oranges and pears than apples.how many fruits are there altogether? 
math
A box contained fruits such as apples, oranges and pears. 3/5 of the fruits were apples. 1/4 of the remaining fruits were oranges and the rest were pears. If there were 60 pears in the box, how many oranges were there? 
Math grade 6, ratio
Mr. Lynch bought some oranges and pears.after giving away 10 oranges, he had twice as many pears as oranges left.if he had 24 pears in the end,what was the ratio of the number of oranges to the number of pears he had at first? 
Mathematics
There were some apples, oranges and pears in a basket. There are 50% more oranges than apples. The ratio of the number of apples to the number of pears was 5:4. (a) Find the ratio of the number of apples to the number of oranges to …