Question

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.

Answer 1

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

$4(5x+2y=25)\\20x+8y=100\ \ \ Eqn\ 3$

Subtracting Eqn 1 from Eqn 3

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

Dividing both sides by 8

$\frac{8x}{8}=\frac{12}{8}\\x=1.5$

Putting x=1.5 in Eqn 1

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

Dividing both sides by 8

$\frac{8y}{8}=\frac{70}{8}\\y=8.75$

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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