MATHEMATICS HIGH SCHOOL

A necklace has and matching bracelet have two types of beads. The necklace has 12 large beads and 8 small beads and weighs 88 grams. The bracelet has 5 large beads and 2 small beads and weighs 25 grams. Write and solve a system of equations to find the weight of a large bead and weight of a small bead.

Answers

Answer 1
Answer:

Weight of one large bead is 1.5 grams and weight of one small bead is 8.75 grams.

Step-by-step explanation:

Let,

Weight of one large bead = x

Weight of one small bead = y

According to given statement;

12x+8y=88     Eqn 1

5x+2y=25      Eqn 2

Multiplying Eqn 2 by 4

4(5x+2y=25)\n20x+8y=100\ \ \ Eqn\ 3\n

Subtracting Eqn 1 from Eqn 3

(20x+8y)-(12x+8y)=100-88\n20x+8y-12x-8y=12\n8x=12

Dividing both sides by 8

(8x)/(8)=(12)/(8)\nx=1.5

Putting x=1.5 in Eqn 1

12(1.5)+8y=88\n18+8y=88\n8y=88-18\n8y=70

Dividing both sides by 8

(8y)/(8)=(70)/(8)\ny=8.75

Weight of one large bead is 1.5 grams and weight of one small bead is 8.75 grams.

Keywords: linear equation, elimination method

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