Given that x = 3, y = 2, and r = 5, work out:
3x² + y² - r²
A shopkeeper packed 5¼ kg of rice into ¼ kg packets. He then sold each packet at Sh 120. How much money did he get altogether?
Answer (2)
The result of the expression 3 x 2 + y 2 − r 2 with given values x=3, y=2, r=5 is 6. The shopkeeper packed 21 packets of 1/4 kg rice and made a total of 2520 Sh by selling them at 120 Sh each.
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Let's solve the problem step-by-step.
The first part of the problem is an algebraic expression that needs to be evaluated:
Given:
x = 3
y = 2
r = 5
The expression to evaluate is: 3 x 2 + y 2 − r 2
Let's calculate each part:
x 2 = 3 2 = 9
y 2 = 2 2 = 4
r 2 = 5 2 = 25
Substitute these values into the expression: 3 ( 9 ) + 4 − 25
Simplify: 27 + 4 − 25 = 31 − 25 = 6
So, the value of the expression is 6.
The second part of the problem deals with a practical situation of selling packets of rice:
The shopkeeper packed 5 4 1 kg of rice into 4 1 kg packets.
Convert 5 4 1 to an improper fraction: 5 4 1 = 4 21 kg
Determine the number of 4 1 kg packets: Number of packets = 4 21 ÷ 4 1 = 21 packets
Each packet is sold at Sh 120. Calculate the total money received: 21 × 120 = 2520
Therefore, the shopkeeper received Sh 2520 altogether.
