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# Word Problems and Systems of Equations

Train Tickets
At the the Pittsburg zoo, children ride a train for 25 cents, adults pay \$1.00, and Senior citizens 75 cents. On a given day, 1400 passengers paid a total of \$740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders.

Manufacturing
Stewart's Metals has three silver alloys on hand. One is 22% silver, another is 30% silver, and the third is 42% silver. HOw many grams of each alloy is required to produce 80 grams of a new alloy that is 34 % silver if the amount of 30% alloy used is twice the amount of 22% alloy used.

Investment
Monica receives an \$80,000 inheritance. She invests part of it in CD's earning 6.7%. APY part in bonds earning 9.3% APY and the remainder in a growth fund earning 15.6% APY. She invests three times as much in the growth fund as in the other two combined. How much does she have in each investment if she receives \$10,843 interest the first year?

Investments
Oscar invests \$20,000 in three investments earning 6% APY,8%APY and 10%APY. He invests \$9000 more in the 10% investment than in the 6% investment. How much does he have invested at each rate if he receives \$1780 interest the first year?

#### Solution Preview

Train tickets
Suppose the number of children, adult and senior rides are x, y and z, respectively. Now we analyze the condition.
1. On a given day, 1400 passengers paid for rides. Then x + y + z = 1400
2. They paid a total of \$740. Then 0.25x + y + 0.75z = 740
3. There were 250 more children riders than all other riders. Then x = (y+z) + 250
Thus we obtain the following system of equations
x + y + ...

#### Solution Summary

Systems of equations are written from word problems. The systems are not solved.

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